Relevant bibliographies by topics / Hyperbolic equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Hyperbolic equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 July 2025

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Journal articles on the topic "Hyperbolic equation"

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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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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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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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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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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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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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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Farg, Ahmed Saeed, A. M. Abd Elbary, and Tarek A. Khalil. "Applied method of characteristics on 2nd 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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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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Dissertations / Theses on the topic "Hyperbolic equation"

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Howard, Tamani M. "Hyperbolic Monge-Ampère Equation." Thesis, University of North Texas, 2006. https://digital.library.unt.edu/ark:/67531/metadc5322/.

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In this paper we use the Sobolev steepest descent method introduced by John W. Neuberger to solve the hyperbolic Monge-Ampère equation. First, we use the discrete Sobolev steepest descent method to find numerical solutions; we use several initial guesses, and explore the effect of some imposed boundary conditions on the solutions. Next, we prove convergence of the continuous Sobolev steepest descent to show local existence of solutions to the hyperbolic Monge-Ampère equation. Finally, we prove some results on the Sobolev gradients that mainly arise from general nonlinear differential equatio
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Vartiainen, Markku Juhani. "Singular boundary element methods for the hyperbolic wave equation." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621821.

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Kruse, Carola. "Regularity and approximation of a hyperbolic-elliptic coupled problem." Thesis, Brunel University, 2010. http://bura.brunel.ac.uk/handle/2438/5253.

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In this thesis, we investigate the regularity and approximation of a hyperbolic-elliptic coupled problem. In particular, we consider the Poisson and the transport equation where both are assigned nonhomogeneous Dirichlet boundary conditions. The coupling of the two problems is executed as follows. The right hand side function of the Poisson equation is the solution ρ of the transport equation whereas the gradient field E = −∇u, with u being solution of the Poisson problem, is the convective field for the transport equation. The analysis is done throughout on a nonconvex, not simply connected d
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Abd, El Wahab Madiha A. "Block diagonal schemes for hyperbolic equation using finite element method." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329374.

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Unterweger, Kristof Gregor [Verfasser]. "High-Performance Coupling of Dynamically Adaptive Grids and Hyperbolic Equation Systems / Kristof Gregor Unterweger." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126296031/34.

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Arjmand, Doghonay. "Analysis and Applications of the Heterogeneous Multiscale Methods for Multiscale Elliptic and Hyperbolic Partial Differential Equations." Licentiate thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-129237.

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This thesis concerns the applications and analysis of the Heterogeneous Multiscale methods (HMM) for Multiscale Elliptic and Hyperbolic Partial Differential Equations. We have gathered the main contributions in two papers. The first paper deals with the cell-boundary error which is present in multi-scale algorithms for elliptic homogenization problems. Typical multi-scale methods have two essential components: a macro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. Solving the micro model requires, on the other hand, imposing boundar
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Knott, Gereon. "Oscillatory Solutions to Hyperbolic Conservation Laws and Active Scalar Equations." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-122808.

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In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.
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Fall, Djiby. "Longtime dynamics of hyperbolic evolutionary equations in ubounded domains and lattice systems." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001053.

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GUIO, ELIAS MARION. "A PRIORI GRADIENT ESTIMATES, EXISTENCE AND NON-EXISTENCE FOR A MEAN CURVATURE EQUATION IN HYPERBOLIC SPACE." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3755@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Um resultado clássico no âmbito de equações diferenciais parciais e de geometria diferencial é o seguinte: Dada uma constante a existe uma condição da fronteira do domínio (Omega) de maneira que o problema de Dirichlet para a equação da curvatura média a no espaço Euclidiano é sempre solúvel. Este é um teorema devido a Serrin (1969). Além disso, se a condição de Serrin não for satisfeita, há um resultado de não-existência. A partir disso foi perguntado se um resultado similar valeria no espaço Hiperbólico. A finalidade d
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Voonna, Kiran. "Development of discontinuous galerkin method for 1-D inviscid burgers equation." ScholarWorks@UNO, 2003. http://louisdl.louislibraries.org/u?/NOD,75.

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Thesis (M.S.)--University of New Orleans, 2003.<br>Title from electronic submission form. "A thesis ... in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical Engineering"--Thesis t.p. Vita. Includes bibliographical references.
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Books on the topic "Hyperbolic equation"

1

Georgiev, Vladimir. Semilinear hyperbolic equations. Mathematical Society of Japan, 2000.

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A, Caffarelli Luis, and E. Weinan 1963-, eds. Hyperbolic equations and frequency interactions. American Mathematical Society, Institute for Advanced Study, 1999.

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Sharma, Vishnu D. Quasilinear hyperbolic systems, compressible flows, and waves. CRC/Taylor & Francis, 2010.

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Scroggs, Jeffrey S. Shock-layer bounds for a singularly perturbed equation. Institute for Computer Applications in Science and Engineering, 1990.

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Petkov, Vesselin. Scattering theory for hyperbolic operators. North-Holland, 1989.

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Petkov, Vesselin. Scattering theory for hyperbolic operators. Universidade Federal de Pernambuco, 1987.

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Osher, Stanley. High order essentially non-oscillatory schemes for Hamilton-Jacobi equations. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Osher, Stanley. High order essentially non-oscillatory schemes for Hamilton-Jacobi equations. National Aeronautics and Space Administration, Langley Research Center, 1990.

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9

A, Mitropolʹskiĭ I͡U. Asimptoticheskie metody issledovanii͡a kvazivolnovykh uravneniĭ giperbolicheskogo tipa. Nauk. dumka, 1991.

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Bidegaray-Fesquet, Brigitte. Hiérarchie de modèles en optique quantique: De Maxwell-Bloch à Schr̈odinger non-linéaire. Springer, 2006.

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Book chapters on the topic "Hyperbolic equation"

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Alinhac, Serge. "The Wave Equation." In Hyperbolic Partial Differential Equations. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_5.

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Zudin, Yuri B. "Hyperbolic Heat Conduction Equation." In Mathematical Engineering. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-53445-8_9.

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Ocłoń, Paweł, and Stanisław Łopata. "Hyperbolic Heat Conduction Equation." In Encyclopedia of Thermal Stresses. Springer Netherlands, 2014. http://dx.doi.org/10.1007/978-94-007-2739-7_390.

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Zudin, Yuri B. "Hyperbolic Heat Conduction Equation." In Mathematical Engineering. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-25167-2_9.

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Cai, Zhenning, Yuwei Fan, and Ruo Li. "Hyperbolic Model Reduction for Kinetic Equations." In SEMA SIMAI Springer Series. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-86236-7_8.

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AbstractWe make a brief historical review of the moment model reduction for the kinetic equations, particularly Grad’s moment method for Boltzmann equation. We focus on the hyperbolicity of the reduced model, which is essential for the existence of its classical solution as a Cauchy problem. The theory of the framework we developed in the past years is then introduced, which preserves the hyperbolic nature of the kinetic equations with high universality. Some lastest progress on the comparison between models with/without hyperbolicity is presented to validate the hyperbolic moment models for r
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Eftimie, Raluca. "One-Equation Local Hyperbolic Models." In Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02586-1_3.

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Alinhac, Serge. "Energy Inequalities for the Wave Equation." In Hyperbolic Partial Differential Equations. Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87823-2_6.

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Giese, Guido. "Decomposition of the Elastic-plastic Wave Equation into Advection Equations." In Hyperbolic Problems: Theory, Numerics, Applications. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8720-5_41.

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Chattot, Jean-Jacques. "Integration of a Linear Hyperbolic Equation." In Scientific Computation. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-05064-4_5.

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Ukai, Seiji, Tong Tang, and Shih-Hsien Yu. "Nonlinear Boundary Layers of the Boltzmann Equation." In Hyperbolic Problems: Theory, Numerics, Applications. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55711-8_8.

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Conference papers on the topic "Hyperbolic equation"

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Herrmann, Leopold. "Hyperbolic diffusion equation." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2009: (ICCMSE 2009). AIP, 2012. http://dx.doi.org/10.1063/1.4772177.

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Jie Sun. "The group schemes for the hyperbolic equation." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002534.

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Savaşaneril, Nurcan Baykuş. "Numerical Solutions of Hyperbolic Partial Differential Equations." In 7th International Students Science Congress. Izmir International guest Students Association, 2023. http://dx.doi.org/10.52460/issc.2023.033.

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Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. In this study, a matrix method based on collocation points and Taylor polynomials is presented to obtain the approximate solution of the hyperbolic partial differential equation. This technique reduces the solution of the mentioned hyperbolic partial differential equation under initial and boundary conditions to the solution of a matrix equation whose Taylor coefficients are unknown. Thus, the approximate solution is obtained in terms of Taylor polynomials. An exa
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Treilande, Tabita, and Ilmars Iltins. "Non-standard method for solving hyperbolic heat equations." In 23rd International Scientific Conference Engineering for Rural Development. Latvia University of Life Sciences and Technologies, Faculty of Engineering and Information Technologies, 2024. http://dx.doi.org/10.22616/erdev.2024.23.tf117.

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In this article, we build upon the pioneering work of Abraham Temkin (1919-2007), who introduced a novel separation of variables method for non-stationary heat conduction in the 1960s. Our extension applies this method to the hyperbolic heat equation, incorporating a relaxation term. The hyperbolic heat equation, a partial differential equation combining features of both hyperbolic and parabolic equations, finds wide applications across various scientific fields, including physics, engineering, geophysics, medical imaging, and more. Our investigation centres on the application of the Temkin’s
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Ashyralyev, Allaberen, Fatma Songul Ozesenli Tetikoglu, and Tulay Kahraman. "Source identification problem for an elliptic-hyperbolic equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959650.

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Wang, Honglei, and Chunhuan Xiang. "Novel Traveling Hyperbolic Function Solution for Evolution Equation." In 2017 2nd International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE 2017). Atlantis Press, 2017. http://dx.doi.org/10.2991/isaeece-17.2017.50.

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Ashyralyev, Allaberen, Faruk Özger, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "The Hyperbolic-Elliptic Equation with the Nonlocal Condition." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636797.

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He, J., and B. Q. Zhang. "The Local Analytic Numerical Method for the Double Vortex Combustor Flow." In ASME 1985 Beijing International Gas Turbine Symposium and Exposition. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-igt-110.

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A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the
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Song, Zhiyao, Honggui Zhang, Jun Kong, Ruijie Li, and Wei Zhang. "An Efficient Numerical Model of Hyperbolic Mild-Slope Equation." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29146.

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Introduction of an effective wave elevation function, the simplest time-dependent hyperbolic mild-slope equation has been presented and an effective numerical model for the water wave propagation has been established combined with different boundary conditions in this paper. Through computing the effective wave elevation and transforming into the real transient wave motion, then related wave heights are computed. Because the truncation errors of the presented model only induced by the dissipation terms, but those of Lin’s model (2004) contributed by the convection terms, dissipation terms and
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Zvonareva, Tatiana, and Olga Krivorotko. "Identifiability Analysis for Source Problem of Quasi-Hyperbolic Equation." In 2023 5th International Conference on Problems of Cybernetics and Informatics (PCI). IEEE, 2023. http://dx.doi.org/10.1109/pci60110.2023.10325964.

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Reports on the topic "Hyperbolic equation"

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Symes, Wiliam W. Trace Regularity for a Second Order Hyperbolic Equation With Nonsmooth Coefficients. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada452695.

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Burns, J. A., and R. H. Fabiano. Feedback Control of a Hyperbolic Partial-Differential Equation with Viscoelastic Damping,. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada192896.

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Popivanov, Petar, and Angela Slavova. Explicit Solutions of the Hyperbolic Monge–Ampere Type Equation, of a Nonlinear Evolution System and Their Qualitative Properties. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2020. http://dx.doi.org/10.7546/crabs.2020.06.03.

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Restrepo, J. M., and G. K. Leaf. Wavelet=Galerkin discretization of hyperbolic equations. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/432435.

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Shearer, Michael. Systems of Hyperbolic Partial Differential Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290287.

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290372.

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Shearer, Michael. Systems of Nonlinear Hyperbolic Partial Differential Equations. Defense Technical Information Center, 1997. http://dx.doi.org/10.21236/ada344449.

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Hale, Jack K., and Nicholas Stavrakakis. Limiting Behavior of Linearly Damped Hyperbolic Equations,. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada170161.

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Keller, H. B., and H. O. Kreiss. Mathematical Software for Hyperbolic Equations and Two Point Boundary Value Problems. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada151982.

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Ekaterinarius, John A. Development of High-Order Methods for Multi-Physics Problems Governed by Hyperbolic Equations. Defense Technical Information Center, 2010. http://dx.doi.org/10.21236/ada542262.

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