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Journal articles on the topic 'Hyperbolic equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Petkov, Emiliyan G. "Development and Implementation of NURBS Models of Quadratic Curves and Surfaces." Serdica Journal of Computing 3, no. 4 (2010): 425–48. http://dx.doi.org/10.55630/sjc.2009.3.425-448.

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This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using th

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2

Assanova, Anar, and Altynai Molybaikyzy. "Solution to the periodic problem for the impulsive hyperbolic equation with discrete memory." Kazakh Mathematical Journal 25, no. 1 (2025): 16–27. https://doi.org/10.70474/kmj-25-1-02.

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In this article, we consider the periodic problem for the impulsive hyperbolic equation with discrete memory. Impulsive hyperbolic equations with discrete memory arise as a mathematical model for describing physical processes in the neural networks, discontinuous dynamical systems, hybrid systems, and etc. Questions of the existence and construction of solutions to periodic problems for impulsive hyperbolic equations with discrete memory remain important issues in the theory of discontinuous partial differential equations. To find the solvability conditions of this problem we apply Dzhumabaev’

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3

Gavrilyuk, Sergey, and Keh-Ming Shyue. "Hyperbolic approximation of the BBM equation." Nonlinearity 35, no. 3 (2022): 1447–67. http://dx.doi.org/10.1088/1361-6544/ac4c49.

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Abstract It is well known that the Benjamin–Bona–Mahony (BBM) equation can be seen as the Euler–Lagrange equation for a Lagrangian expressed in terms of the solution potential. We approximate the Lagrangian by a two-parameter family of Lagrangians depending on three potentials. The corresponding Euler–Lagrange equations can be then written as a hyperbolic system of conservations laws. The hyperbolic BBM system has two genuinely nonlinear eigenfields and one linear degenerate eigenfield. Moreover, it can be written in terms of Riemann invariants. Such an approach conserves the variational struc

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Al-Muhiameed, Zeid I. A., and Emad A. B. Abdel-Salam. "Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/265348.

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With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parametersp

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5

Camurdan, Mehmet. "Uniform stabilization of a coupled structural acoustic system by boundary dissipation." Abstract and Applied Analysis 3, no. 3-4 (1998): 377–400. http://dx.doi.org/10.1155/s108533759800061x.

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We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic Kirchoff equation. These two hyperbolic equations are coupled by appropriate trace operators. This overall model differs from those previously studied in the literature in that the elastic chamber floor

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6

Kehaili, Abdelkader, Ali Hakem, and Abdelkader Benali. "Homotopy Perturbation Transform method for solving the partial and the time-fractional differential equations with variable coefficients." Global Journal of Pure and Applied Sciences 26, no. 1 (2020): 35–55. http://dx.doi.org/10.4314/gjpas.v26i1.6.

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In this paper, we present the exact solutions of the Parabolic-like equations and Hyperbolic-like equations with variable coefficients, by using Homotopy perturbation transform method (HPTM). Finally, we extend the results to the time-fractional differential equations. Keywords: Caputo’s fractional derivative, fractional differential equations, homotopy perturbation transform method, hyperbolic-like equation, Laplace transform, parabolic-like equation.

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7

Kranysˇ, M. "Causal Theories of Evolution and Wave Propagation in Mathematical Physics." Applied Mechanics Reviews 42, no. 11 (1989): 305–22. http://dx.doi.org/10.1115/1.3152415.

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There are still many phenomena, especially in continuum physics, that are described by means of parabolic partial differential equations whose solution are not compatible with the causality principle. Compatibility with this principle is required also by the theory of relativity. A general form of hyperbolic operators for the most frequently occurring linear governing equations in mathematical physics is written down. It is then easy to convert any given parabolic equation to the hyperbolic form without necessarily entering into the cause of the inadequacy of the governing equation. The method

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8

Zheng, Zhao, and Yu Xuegang. "Hyperbolic Schrödinger equation." Advances in Applied Clifford Algebras 14, no. 2 (2004): 207–13. http://dx.doi.org/10.1007/s00006-004-0016-2.

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9

Farg, Ahmed Saeed, A. M. Abd Elbary, and Tarek A. Khalil. "Applied method of characteristics on 2^nd order linear P.D.E." Journal of Physics: Conference Series 2304, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2304/1/012003.

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Abstract PDEs are very important in dynamics, aerodynamics, elasticity, heat transfer, waves, electromagnetic theory, transmission lines, quantum mechanics, weather forecasting, prediction of crime places, disasters, how universe behave ……. Etc., second order linear PDEs can be classified according to the characteristic equation into 3 types hyperbolic, parabolic and elliptic; Hyperbolic equations have two distinct families of (real) characteristic curves, parabolic equations have a single family of characteristic curves, and the elliptic equations have none. All the three types of equations c

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10

Kubera, P., and J. Felcman. "On a numerical flux for the pedestrian flow equations." Journal of Applied Mathematics, Statistics and Informatics 11, no. 2 (2015): 79–96. http://dx.doi.org/10.1515/jamsi-2015-0014.

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Abstract The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic

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11

Korzyuk, V. I., and E. S. Cheb. "CAUCHY PROBLEM FOR A LINEAR HYPERBOLIC EQUATION OF THE SECOND ORDER." Mathematical Modelling and Analysis 11, no. 3 (2006): 275–94. http://dx.doi.org/10.3846/13926292.2006.9637318.

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The definition of hyperbolic equation by a prescribed vector field is introduced for linear differential equation of the second order. The Cauchy problem with prescribed boundary conditions is considered for such equations. The theorems of existence and uniqueness of a strong solution to the given problem are proved by the method of energy inequalities and mollifiers with variable step. Key words: hyperbolic equation, Cauchy problem, strong solution, energy inequality, mollifiers.

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12

Mahomed, F. M., A. Qadir, and A. Ramnarain. "Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods." Mathematical Problems in Engineering 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/202973.

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In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs) in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE) into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revi

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13

Ashyralyev, A., and B. Haso. "Stability of the time-dependent identification problem for delay hyperbolic equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 107, no. 3 (2022): 25–34. http://dx.doi.org/10.31489/2022m3/25-34.

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Time-dependent and space-dependent source identification problems for partial differential and difference equations take an important place in applied sciences and engineering, and have been studied by several authors. Moreover, the delay appears in complicated systems with logical and computing devices, where certain time for information processing is needed. In the present paper, the time-dependent identification problem for delay hyperbolic equation is investigated. The theorems on the stability estimates for the solution of the time-dependent identification problem for the one dimensional

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14

Shishkina, E. L. "General Euler-Poisson-Darboux Equation and Hyperbolic B-Potentials." Contemporary Mathematics. Fundamental Directions 65, no. 2 (2019): 157–338. http://dx.doi.org/10.22363/2413-3639-2019-65-2-157-338.

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In this work, we develop the theory of hyperbolic equations with Bessel operators. We construct and invert hyperbolic potentials generated by multidimensional generalized translation. Chapter 1 contains necessary notation, deﬁnitions, auxiliary facts and results. In Chapter 2, we study some generalized weight functions related to a quadratic form. These functions are used below to construct fractional powers of hyperbolic operators and solutions of hyperbolic equations with Bessel operators. Chapter 3 is devoted to hyperbolic potentials generated by multidimensional generalized translation. Th

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15

Ashyralyev, Allaberen, and Ozgur Yildirim. "A Note on the Second Order of Accuracy Stable Difference Schemes for the Nonlocal Boundary Value Hyperbolic Problem." Abstract and Applied Analysis 2012 (2012): 1–29. http://dx.doi.org/10.1155/2012/846582.

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The second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value hyperbolic problem for the differential equations in a Hilbert spaceHwith the self-adjoint positive definite operatorA. The stability estimates for the solutions of these difference schemes are established. In practice, one-dimensional hyperbolic equation with nonlocal boundary conditions and multidimensional hyperbolic equation with Dirichlet conditions are considered. The stability estimates for the solutions of these difference schemes for the nonlocal boundary value hyperbolic pr

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16

Ashyralyev, Allaberen, and Deniz Agirseven. "Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations." Mathematics 7, no. 12 (2019): 1163. http://dx.doi.org/10.3390/math7121163.

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In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential problem for a semilinear hyperbolic equation with unbounded time delay term is established. In applications, the existence and uniqueness of bounded solutions of four problems for semilinear hyperbolic equations with time delay in unbounded term are obtained. For the approximate solution of this abstract differential problem, the two-step differen

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17

Pandir, Yusuf, and Halime Ulusoy. "New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/201276.

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We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very

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18

Candemir, Nuray, Murat Tanışlı, Kudret Özdaş, and Süleyman Demir. "Hyperbolic Octonionic Proca-Maxwell Equations." Zeitschrift für Naturforschung A 63, no. 1-2 (2008): 15–18. http://dx.doi.org/10.1515/zna-2008-1-203.

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In this study, after introducing the hyperbolic octonionic (counteroctonion) algebra, which is also expressed in the sub-algebra of sedenions, and differential operator, Proca-Maxwell equations and relevant field equations are derived in compact, simpler and elegant forms using hyperbolic octonions. This formalism demonstrates that Proca-Maxwell equations can be expressed in a single equation.

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19

Aldashev, S. A. "TRICOMI PROBLEM FOR MULTIDIMENSIONAL MIXED HYPERBOLIC-PARABOLIC EQUATION." Vestnik of Samara University. Natural Science Series 26, no. 4 (2021): 7–14. http://dx.doi.org/10.18287/2541-7525-2020-26-4-7-14.

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It is known that in mathematical modeling of electromagnetic fields in space, the nature of the electromagnetic process is determined by the properties of the media. If the medium is non-conducting, then we obtain multidimensional hyperbolic equations. If the mediums conductivity is higher, then we arrive at multidimensional parabolic equations. Consequently, the analysis of electromagnetic fields in complex media (for example, if the conductivity of the medium changes) reduces to multidimensional hyperbolic-parabolic equations. When studying these applications, one needs to obtain an explicit

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20

Zayed, E. M. E., and Shorog Al-Joudi. "Applications of an Extended -Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics." Mathematical Problems in Engineering 2010 (2010): 1–19. http://dx.doi.org/10.1155/2010/768573.

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We construct the traveling wave solutions of the (1+1)-dimensional modified Benjamin-Bona-Mahony equation, the (2+1)-dimensional typical breaking soliton equation, the (1+1)-dimensional classical Boussinesq equations, and the (2+1)-dimensional Broer-Kaup-Kuperschmidt equations by using an extended -expansion method, whereGsatisfies the second-order linear ordinary differential equation. By using this method, new exact solutions involving parameters, expressed by three types of functions which are hyperbolic, trigonometric and rational function solutions, are obtained. When the parameters are t

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21

M. S. Al-Amry and H. S. Bafarag. "Extended Hyperbolic Function Method to Solve Two New Nonlinear Partial Differential Equations." University of Aden Journal of Natural and Applied Sciences 28, no. 2 (2025): 97–105. https://doi.org/10.47372/uajnas.2024.n2.a09.

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In this paper, we present two new equations, firstly a combined of Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation with modified Korteweg-de Vries-Benjamin-Bona-Mahony m(KdV-BBM) and denoted by c((KdV-BBM)-m(KdV-BBM)), secondly a combined of Shallow Water Wave-Ablowitz-Kaup-Newell-Segur (SWW-AKNS) equation with Equal-Width (EW) equation and denoted by c((SWW-AKNS)-EW). Then we apply the extended hyperbolic function method (EHFM) to solve the new equations. Exact traveling wave solutions are obtained and expresses in terms of hyperbolic functions and trigonometric functions.

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22

Alakashi, Abobaker Mohammed, and Bambang Basuno. "Comparison between Cell-Centered Schemes Computer Code and Fluent Software for a Transonic Flow Pass through an Array of Turbine Stator Blades." Applied Mechanics and Materials 437 (October 2013): 271–74. http://dx.doi.org/10.4028/www.scientific.net/amm.437.271.

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The Finite Volume Method (FVM) is a discretization method which is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws; it has been extensively used in several engineering fields. The Finite volume method uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [. the developed computer code based Cell-centered scheme and Fluent software had been used to investigate the inviscid Transonic Flow Pass Through an array of Turbine Stator Blades. The governing e

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23

Syazana Saharizan, Nur, and Nurnadiah Zamri. "Numerical solution for a new fuzzy transform of hyperbolic goursat partial differential equation." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 1 (2019): 292. http://dx.doi.org/10.11591/ijeecs.v16.i1.pp292-298.

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<p>The main objective of this paper is to present a new numerical method with utilization of fuzzy transform in order to solve various engineering problems that represented by hyperbolic Goursat partial differentical equation (PDE). The application of differential equations are widely used for modelling physical phenomena. There are many complicated and dynamic physical problems involved in developing a differential equation with high accuracy. Some problems requires a complex and time consuming algorithms. Therefore, the application of fuzzy mathematics seems to be appropriate for solvi

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24

Gadjiev, Tahir, Rafig Rasulov, and Orkhan Aliev. "On Behavior of Solution of Degenerated Hyperbolic Equation." ISRN Applied Mathematics 2012 (November 1, 2012): 1–10. http://dx.doi.org/10.5402/2012/124936.

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The purpose of this paper is to learn some features of hyperbolic type of nonlinear equations. It is shown that the solution of the equation approaches to the endlessness in the inside of some initial conditions and time of the special marks. The local existence of the equation’s solution has been proved and the problem of unlimited increasing on the solution of nonlinear hyperbolic equations type during the finite time is investigated.

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25

Khubiev, K. U. "Analogue of Tricomi problem for one characteristically loaded hyperbolic-parabolic equation." ADYGHE INTERNATIONAL SCIENTIFIC JOURNAL 23, no. 4 (2023): 54–61. http://dx.doi.org/10.47928/1726-9946-2023-23-4-54-61.

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In this paper considers an analogue of the Trikomi problem for one characteristically loaded model equation of the mixed hyperbolo-parabolic type of the second order. The loaded term in the domain of the hyperbolic function is the derivative of the desired function trace on characteristics of the equation of the same order as the equation itself. Sufficient conditions on the coefficients are found for a unique solution.

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26

Al-Amry, M. S., and E. F. Al-Abdali. "New Exact Solutions for Generalized of Combined with Negative Calogero-Bogoyavlenskii Schiff and Generalized Yu–Toda–Sassa–Fukuyama Equations." University of Aden Journal of Natural and Applied Sciences 28, no. 1 (2024): 25–30. http://dx.doi.org/10.47372/uajnas.2024.n1.a04.

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In this paper, we present generalized model of combined Calogero-Bogoyavlenskii Schiff and negative-order Calogero-Bogoyavlenskii Schiff G(CBS-nCBS) equation and generalized Yu–Toda–Sassa–Fukuyama g(YTSF) equation. We apply the extended hyperbolic function method, to solve generalized models. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions solutions of these equations from the method with the aid of the computer program Maple.

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27

Abdumitalip uulu, K. "Boundary Value Problems for a Mixed Fourth-order Parabolic-Hyperbolic Equation With Discontinuous Gluing Conditions." Bulletin of Science and Practice, no. 11 (November 15, 2022): 12–23. http://dx.doi.org/10.33619/2414-2948/84/01.

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The theorem of the existence and uniqueness of the solution of the boundary value problem for the equation in partial derivatives of the fourth order with variable coefficients containing the product of the mixed parabolic-hyperbolic operator and the differential operator of the oscillation string with discontinuous conditions of gluing in the pentagon to the plane is proved. By the method of reducing the order of equations, the solvability of the boundary value problem is reduced to the solution of the Tricomi problem for the mixed parabola-hyperbolic equation with variable coefficients and d

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28

Syukron, Ahmad Aftah, and Isnaini Lilis Elviyanti. "Solusi Persamaan Schrodinger dengan Potensial Scraf II Hyperbolic menggunakan Pendekatan Semiklasik." JURNAL KRIDATAMA SAINS DAN TEKNOLOGI 4, no. 01 (2022): 87–92. http://dx.doi.org/10.53863/kst.v4i01.523.

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The particle system is affected by the Scraf II Hyperbolic potential. The solution for solving the Schrodinger equation with the Scraff II Hyperbolic potential uses a semiclassical approach, namely using the WKB approach. The WKB approach is used to obtain an equation for the energy spectrum that is affected by the Scraf II Hyperbolic potential. Keywords: The Schrodinger equation, Hyperbolic Scraf II potential, WKB approach

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29

Lin, Ching-Lung, Liren Lin, and Gen Nakamura. "Born approximation and sequence for hyperbolic equations." Asymptotic Analysis 121, no. 2 (2021): 101–23. http://dx.doi.org/10.3233/asy-201596.

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The Born approximation and the Born sequence are considered for hyperbolic equations when we perturb their leading parts. The Born approximation is a finite successive approximation such as the finite terms Neumann series for the solution of a hyperbolic equation in terms of the smallness of the perturbation and if the successive approximation is infinitely many times, then we have the Born series. Due to the so called regularity loss for solutions of hyperbolic equations, we need to assume that data such as the inhomogeneous term of the equation, Cauchy datum and boundary datum are C ∞ , and

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30

Koellermeier, Julian, and Manuel Torrilhon. "Numerical Study of Partially Conservative Moment Equations in Kinetic Theory." Communications in Computational Physics 21, no. 4 (2017): 981–1011. http://dx.doi.org/10.4208/cicp.oa-2016-0053.

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AbstractMoment models are often used for the solution of kinetic equations such as the Boltzmann equation. Unfortunately, standard models like Grad's equations are not hyperbolic and can lead to nonphysical solutions. Newly derived moment models like the Hyperbolic Moment Equations and the Quadrature-Based Moment Equations yield globally hyperbolic equations but are given in partially conservative form that cannot be written as a conservative system.In this paper we investigate the applicability of different dedicated numerical schemes to solve the partially conservative model equations. Cause

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31

Cai, Zhenning, Yuwei Fan, Ruo Li, and Zhonghua Qiao. "Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision." Communications in Computational Physics 15, no. 5 (2014): 1368–406. http://dx.doi.org/10.4208/cicp.220313.281013a.

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AbstractWe develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved pro

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32

Domoshnitsky, Alexander. "About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations." gmj 10, no. 3 (2003): 495–502. http://dx.doi.org/10.1515/gmj.2003.495.

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Abstract In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value problem for the heat equation: the maximum principle is not valid, unbounded solutions appear while all solutions of the classical Dirichlet problem tend to zero at infinity, for “narrow enough zones” all solutions oscill

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Ketcheson, David I., and Abhijit Biswas. "Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation." Nonlinearity 38, no. 5 (2025): 055002. https://doi.org/10.1088/1361-6544/adc6e8.

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Abstract We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are potentially useful as analytical or computational tools for understanding the corresponding higher-order equation. We perform a systematic analysis of a family of linear model equations and show that for each member of this family there is a stable hyperbolic approximation whose solution converges to that of the model equation in a certain limit. We th

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Pirmatov, A., T. Isakov, and U. Saktanov. "Conjunction Problems for a Pseudo-hyperbolic Equation of the Fourth Order with Discontinuous Coefficients." Bulletin of Science and Practice 10, no. 12 (2024): 14–21. https://doi.org/10.33619/2414-2948/109/01.

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The relevance of the study is justified by proving the correctness of the conjugation problem for a pseudo-hyperbolic fourth-order equation with discontinuous coefficients. In this work, the methods of Green's function and integral equations are employed to demonstrate the existence and uniqueness of solutions for the first boundary value problem of the pseudo-hyperbolic fourth-order partial differential equation. The obtained results can be applied in the education of students and graduate students in mathematical disciplines.

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35

Bai, C., and A. S. Lavine. "On Hyperbolic Heat Conduction and the Second Law of Thermodynamics." Journal of Heat Transfer 117, no. 2 (1995): 256–63. http://dx.doi.org/10.1115/1.2822514.

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For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This sch

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36

Adomian, G. "Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations." International Journal of Mathematics and Mathematical Sciences 12, no. 1 (1989): 137–43. http://dx.doi.org/10.1155/s0161171289000190.

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The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques. We consider first a nonlinear dissipative wave equation; second, a nonlinear equation modeling convectlon-diffusion processes; and finally, an elliptic partial differential equation.

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Tokibetov, Zh A., N. E. Bashar, and А. К. Pirmanova. "THE CAUCHY-DIRICHLET PROBLEM FOR A SYSTEM OF FIRST-ORDER EQUATIONS." BULLETIN Series of Physics & Mathematical Sciences 72, no. 4 (2020): 68–72. http://dx.doi.org/10.51889/2020-4.1728-7901.10.

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For a single second-order elliptic partial differential equation with sufficiently smooth coefficients, all classical boundary value problems that are correct for the Laplace equations are Fredholm. The formulation of classical boundary value problems for the laplace equation is dictated by physical applications. The simplest of the boundary value problems for the Laplace equation is the Dirichlet problem, which is reduced to the problem of the field of charges distributed on a certain surface. The Dirichlet problem for partial differential equations in space is usually called the Cauchy-Diric

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Zheng, Xiaoxiao, Yadong Shang, and Yong Huang. "Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/109690.

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This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used

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Pratiwi, Indah Nur, Mohammad Syamsu Rosid, and Humbang Purba. "Reducing Residual Moveout for Long Offset Data in VTI Media Using Padé Approximation." E3S Web of Conferences 125 (2019): 15005. http://dx.doi.org/10.1051/e3sconf/201912515005.

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Modification of the hyperbolic travel time equation into non-hyperbolic travel time equation is important to increase the reduction residual moveout for long offset data. Some researchers have modified hyperbolic travel time equation into a non-hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large offset to depth ratio (ODR) so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of error residue at long offset data using Padé approximati

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Avalos, George. "The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics." Abstract and Applied Analysis 1, no. 2 (1996): 203–17. http://dx.doi.org/10.1155/s1085337596000103.

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We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domainΩ, coupled to a “parabolic–like” beam equation holding on∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity e

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Mansimov, K. B., and R. O. Mastaliyev. "Representation of the Solution of Goursat Problem for Second Order Linear Stochastic Hyperbolic Differential Equations." Bulletin of Irkutsk State University. Series Mathematics 36 (2021): 29–43. http://dx.doi.org/10.26516/1997-7670.2021.36.29.

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The article considers second-order system of linear stochastic partial differential equations of hyperbolic type with Goursat boundary conditions. Earlier, in a number of papers, representations of the solution Goursat problem for linear stochastic equations of hyperbolic type in the classical way under the assumption of sufficient smoothness of the coefficients of the terms included in the right-hand side of the equation were obtained. Meanwhile, study of many stochastic applied optimal control problems described by linear or nonlinear second-order stochastic differential equations, in partia

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Aldashev, S. A. "Well-posedness of the main mixed problem for the multidimensional Lavrentiev — Bitsadze equation." Vestnik of Samara University. Natural Science Series 27, no. 3 (2022): 7–13. http://dx.doi.org/10.18287/2541-7525-2021-27-3-7-13.

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It is known that the oscillations of elastic membranes in space are modelled with partial differential equations. If the deflection of the membrane is considered as a function of u(x; t); x = (x1; :::; xm);m 2; then, according to the Hamilton principle, we arrive to a multidimensional wave equation.Assuming that the membrane is in equilibrium in the bending position, we also obtain the multidimensional Laplace equation from the Hamiltons principle.Consequently, the oscillations of elastic membranes in space can be modelled with a multidimensional Lavrentiev Bitsadze equation.The main mixed pro

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Tian, Mengtao, Baohua Guo, Zhezhe Zhang, Chuangwei Zhu, and Pengbo Zhong. "Study on Optimal Conventional Triaxial Strength Criterion of Rock Based on Gauss-Newton Method." E3S Web of Conferences 631 (2025): 01002. https://doi.org/10.1051/e3sconf/202563101002.

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Conventional triaxial strength criteria are used widely to judge the rock failure states. In this paper, the nonlinear least squares method (Guass-newton method) is used to fit the regression relationships between the maximum principal stress σ1 as well as the differential stress σ1-σ3 and the minimum principal stress σ3 by the linear, parabolic, power, logarithmic, hyperbolic and exponential equations in the principal stress space by using 1stOpt software. Results show that the linear equation has a poor fitting effect (low R2), while power, logarithmic, hyperbolic, and exponential equations

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Ayeni, B. J. "Parameter Estimation for Hyperbolic Decline Curve." Journal of Energy Resources Technology 111, no. 4 (1989): 279–83. http://dx.doi.org/10.1115/1.3231437.

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The problem of estimating the nonlinear parameters associated with the hyperbolic decline curve equation is considered in this paper. Estimation equations are developed to estimate these nonlinear parameters. The condition under which the results can be used to predict future oil productions is examined using actual field data. An approximate linear term is obtained from the nonlinear hyperbolic equation through Taylor’s series expansion, and the optimum parameter values are determined by employing the method of least squares through an iterative process. The estimated parameters are incorpora

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Chen, Yong, and Qi Wang. "Exact Complexiton Solutions of the (2+1)-Dimensional Burgers Equation." Zeitschrift für Naturforschung A 60, no. 10 (2005): 673–80. http://dx.doi.org/10.1515/zna-2005-1001.

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Based on two different Riccati equations with different parameters, many new types of complexiton solutions to the (2+1)-dimensional Burgers equation are investigated. Such complexiton solutions obtained possess various combinations of trigonometric periodic and hyperbolic function solutions, various combinations of trigonometric periodic and rational function solutions, various combinations of hyperbolic and rational function solutions. - PACS numbers: 02.30.Ik, 05.45.Yv

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Ruziev, Menglibay, Roman Parovik, Rakhimjon Zunnunov, and Nargiza Yuldasheva. "Non-Local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation." Fractal and Fractional 8, no. 9 (2024): 538. http://dx.doi.org/10.3390/fractalfract8090538.

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This research explores nonlocal problems associated with fractional diffusion equations and degenerate hyperbolic equations featuring singular coefficients in their lower-order terms. The uniqueness of the solution is established using the energy integral method, while the existence of the solution is equivalently reduced to solving Volterra integral equations of the second kind and a fractional differential equation. The study focuses on a mixed domain where the parabolic section aligns with the upper half-plane, and the hyperbolic section is bounded by two characteristics of the equation und

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Guarendi, Andrew N., and Abhilash J. Chandy. "Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions." Scientific World Journal 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/672187.

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We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confir

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López Molina, Juan A., María J. Rivera, and Enrique Berjano. "Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (2014): 20140547. http://dx.doi.org/10.1098/rspa.2014.0547.

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Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impedi

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Temirbekov, N. М., S. I. Kabanikhin, L. N. Тemirbekova, and Zh E. Demeubayeva. "Gelfand-Levitan integral equation for solving coefficient inverse problem." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 85, no. 3 (2022): 158–67. http://dx.doi.org/10.47533/2020.1606-146x.184.

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In this paper, numerical methods for solving multidimensional equations of hyperbolic type by the Gelfand-Levitan method are proposed and implemented. The Gelfand-Levitan method is one of the most widely used in the theory of inverse problems and consists in reducing a nonlinear inverse problem to a one-parameter family of linear Fredholm integral equations of the first and second kind. In the class of generalized functions, the initial-boundary value problem for a multidimensional hyperbolic equation is reduced to the Goursat problem. Discretization and numerical implementation of the direct

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Ikehata, Ryo. "L²‐convergence results for linear dissipative wave equations in unbounded domains." Asymptotic Analysis 36, no. 1 (2003): 63–74. https://doi.org/10.3233/asy-2003-590.

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Hyperbolic linear Cauchy problem εu″+Au+u′=0, u(0)=u0, u′(0)=u1, with “nonnegative” selfadjoint operator A in a real Hilbert space H is first considered. It is shown that the solution uε tends to some solution v as ε↓0 for the parabolic equation v′+Av=0 in a certain sense. Some applications are given. Finally, we present hyperbolic‐hyperbolic convergence results such as the solution for the damped wave equations goes to some solution for the free wave equations as the effect of the damping vanishes in a concrete context.

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