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Journal articles on the topic 'Quasi Linear Equation'

Author: Grafiati

Published: 27 January 2023

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1

Yermachenko, I. "MULTIPLE SOLUTIONS OF THE FOURTH‐ORDER EMDEN‐FOWLER EQUATION." Mathematical Modelling and Analysis 11, no. 3 (September 30, 2006): 347–56. http://dx.doi.org/10.3846/13926292.2006.9637322.

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Two-point boundary value problems for the fourth-order Emden-Fowler equation are considered. If the given equation can be reduced to a quasi‐linear one with a non‐resonant linear part so that both equations are equivalent in some domain D, and if solution of the quasi‐linear problem is located in D, then the original problem has a solution. We show that a quasi‐linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

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2

FRICKE, J. ROBERT. "QUASI-LINEAR ELASTODYNAMIC EQUATIONS FOR FINITE DIFFERENCE SOLUTIONS IN DISCONTINUOUS MEDIA." Journal of Computational Acoustics 01, no. 03 (September 1993): 303–20. http://dx.doi.org/10.1142/s0218396x93000160.

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The linear elastodynamic equations are ill-posed for models which contain high contrast density discontinuities. This paper presents a quasi-linear superset of the linear equations that is well-posed for this situation. The extended system contains a conservation of mass equation and a quasi-linear convective term in the momentum equation. Density, momentum, and stress are the field variables in the quasi-linear system, which is cast in a first order form. Using a Lax–Wendroff finite difference approximation, the utility of the quasi-linear system is demonstrated by modeling underwater acoustic scattering from a truncated ice sheet. The model contains air, ice, and water with a density contrast between air and ice or water of O(103). Superlinear convergence of the Lax–Wendroff scheme is demonstrated for his heterogeneous medium problem.

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3

Everitt, W. N. "A note on linear ordinary quasi-differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 101, no. 1-2 (1985): 1–14. http://dx.doi.org/10.1017/s0308210500026111.

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SynopsisThe theory of differential equations is largely concerned with properties of solutions of individual, or classes of, equations. This paper is given over to the converse problem - that of seeking properties of functions which require them to be, in some respect, solutions of a differential equation, and to determining all possible such differential equations.From this point of view this paper discusses only linear ordinary quasi-differential equations of the second order. However, the methods can be extended to quasi-differential equations of general order.

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4

Sun, Yingte, and Xiaoping Yuan. "Quasi-periodic solution of quasi-linear fifth-order KdV equation." Discrete & Continuous Dynamical Systems - A 38, no. 12 (2018): 6241–85. http://dx.doi.org/10.3934/dcds.2018268.

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5

Fu, Zhongjun, Jianyu Wang, Yun Ou, Genyuan Zhou, and Xiaorong Zhao. "A Linear-Correction Algorithm for Quasi-Synchronous DFT." Mathematical Problems in Engineering 2018 (December 27, 2018): 1–9. http://dx.doi.org/10.1155/2018/1268905.

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Spectral leakage in the harmonic measured by quasi-synchronous DFT (QSDFT) is mainly due to short-range leakage caused by deviation in the signal frequency. By analysing the short-range-leakage characteristic of QSDFT, a linear-correction algorithm (LCQS) for QSDFT’s harmonic-analysis results is proposed. LCQS contains two linear-correction equations: an amplitude-correction equation and an initial-phase-angle-correction equation. The former is constructed by the least-squares method, whereas the latter is generated based on the linear error characteristic of the QSDFT harmonic phase. Simulation and experimental results indicate that this proposed algorithm can efficiently increase the accuracy of the harmonic parameters over a wide frequency range by minimizing the short-range spectral leakage.

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6

Catino, Francesco, and Maria Maddalena Miccoli. "Construction of quasi-linear left cycle sets." Journal of Algebra and Its Applications 14, no. 01 (September 10, 2014): 1550001. http://dx.doi.org/10.1142/s0219498815500012.

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In this paper, we produce a method to construct quasi-linear left cycle sets A with Rad (A) ⊆ Fix (A). Moreover, among these cycle sets, we give a complete description of those for which Fix (A) = Soc (A) and the underlying additive group is cyclic. Using such cycle sets, we obtain left non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation which are different from those obtained in [P. Etingof, T. Schedler and A. Soloviev, Set-theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999) 169–209; P. Etingof, A. Soloviev and R. Guralnick, Indecomposable set-theoretical solutions to the quantum Yang–Baxter equation on a set with a prime number of elements, J. Algebra 242 (2001) 709–719].

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7

Pivovarov, Michail L. "Steady-state solutions of Minorsky’s quasi-linear equation." Nonlinear Dynamics 106, no. 4 (October 7, 2021): 3075–89. http://dx.doi.org/10.1007/s11071-021-06944-9.

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8

Maia, L. A., J. C. Oliveira Junior, and R. Ruviaro. "A quasi-linear Schrödinger equation with indefinite potential." Complex Variables and Elliptic Equations 61, no. 4 (January 18, 2016): 574–86. http://dx.doi.org/10.1080/17476933.2015.1106483.

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9

Dikhaminjia, N., J. Rogava, and M. Tsiklauri. "Operator Splitting for Quasi-Linear Abstract Hyperbolic Equation." Journal of Mathematical Sciences 218, no. 6 (September 28, 2016): 737–41. http://dx.doi.org/10.1007/s10958-016-3058-9.

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10

Belokursky, M. S. "Periodic and almost periodic solutions of the Riccati equations with linear reflecting function." Doklady of the National Academy of Sciences of Belarus 66, no. 5 (November 2, 2022): 479–88. http://dx.doi.org/10.29235/1561-8323-2022-66-5-479-488.

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The method of Mironenko’s reflecting function is used for investigation of Riccati equations. The class of Riccati equations with certain-type reflecting function has been preliminarily constructed. The necessary and sufficient conditions, under which the Riccati equation would have a reflecting function linear in phase variable, are proved. These conditions are constructive in nature, since on their basis the formula is obtained, which shows the linear in phase variable reflecting function in terms of the coefficients of the Riccati equation. Additionally, the relationship between the parity (oddness) property of the coefficients of the Riccati equation and the existence of a reflecting function linear in phase variable is investigated. The application of the method of Mironenko’s reflecting function to the constructed class of Riccati equations revealed sufficient conditions, under which all its solutions are periodic or almost periodic. A sign of no periodic solutions for almost periodic Riccati equations is obtained. An example of the quasi-periodic Riccati equation with quasi-periodic reflecting function, which has a periodic solution, is given.

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11

Zhdanov, Michael S., Sheng Fang, and Gábor Hursán. "Electromagnetic inversion using quasi‐linear approximation." GEOPHYSICS 65, no. 5 (September 2000): 1501–13. http://dx.doi.org/10.1190/1.1444839.

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Three‐dimensional electromagnetic inversion continues to be a challenging problem in electrical exploration. We have recently developed a new approach to the solution of this problem based on quasi‐linear approximation of a forward modeling operator. It generates a linear equation with respect to the modified conductivity tensor, which is proportional to the reflectivity tensor and the complex anomalous conductivity. We solved this linear equation by using the regularized conjugate gradient method. After determining a modified conductivity tensor, we used the electrical reflectivity tensor to evaluate the anomalous conductivity. Thus, the developed inversion scheme reduces the original nonlinear inverse problem to a set of linear inverse problems. The developed algorithm has been realized in computer code and tested on synthetic 3-D EM data. The case histories include interpretation of a 3-D magnetotelluric survey conducted in Hokkaido, Japan, and the 3-D inversion of the tensor controlled‐source audio magnetotelluric data over the Sulphur Springs thermal area, Valles Caldera, New Mexico, U.S.A.

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12

Paola, M. Di. "Linear Systems Excited by Polynomials of Filtered Poission Pulses." Journal of Applied Mechanics 64, no. 3 (September 1, 1997): 712–17. http://dx.doi.org/10.1115/1.2788955.

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The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equation that can be exactly solved.

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13

Alexandrikova, T. A., and M. P. Galanin. "NONLINEAR MONOTONIZATION OF THE BABENKO SCHEME FOR THE QUASI‐LINEAR ADVECTION EQUATION." Mathematical Modelling and Analysis 10, no. 2 (June 30, 2005): 113–26. http://dx.doi.org/10.3846/13926292.2005.9637276.

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The paper is devoted to construction and development of new method for numerical solution of hyperbolic type equations [14, 17]. In the previous papers [4, 5, 6, 7, 8, 9] authors have investigated theoretically and tested experimentally 26 different finite‐difference schemes on 4 point patterns for the simplest hyperbolic equation: linear advection equation. This equation has the main features of every hyperbolic equation and is the important part of many mathematical models. In other cases the advection operator is the important part of the full operator of the problem. All 26 schemes have been compared experimentally on the special representative set of tests. Nevertheless to simplicity of the equation, almost all schemes have different disadvantages. They are discussed in detail in the cited papers. So, the investigation of new schemes for this equation is still an important task. In [4, 5, 6, 7, 8, 9] some new schemes were constructed for solving this advection equation. The nonlinear monotone Babenko scheme ("square") proved to be the best among all 26 schemes. So, it is a big interest to generalize this scheme to more difficult equations. The important example is a quasi‐linear advection equation. In this paper our basic aim is to construct a quasi‐monotone nonlinear Babenko scheme for solving the quasi‐linear advection equation and to test it experimentally. The monotonisation of the scheme is done by adding the artificial diffusion with limiters. We also present advanced results of comparative analysis of the new scheme with other known schemes. We have considered explicit and implicit upwind approximation schemes [4, 6, 13, 16] which is firstorder accurate in time and space, the Lax‐Wendroff scheme [4] which is the first order accurate in time and second order accurate in space. We also analyze the monotonised “Cabaret” scheme proposed in [10, 11]. It is second order accurate in time and space, and its monotonisation is based on apriori knowledge of the dependence region of the exact solution. The authors of this scheme called it by “jumping advection”. The considered schemes are compared numerically by using a set of tests, which is similar to one used in [4, 5, 6, 8]. Šiame straipsnyje pasiūlyta kvazi‐monotonie netiesine Babenkos skirtumu schema kvazitiesinei pernešimo lygčiai spresti. Schemos monotoniškumas pasiekiamas pridedant dirbtine difuzija su apribojimais. Pateiktas šios schemos palyginimas su kitomis schemomis. Taip pat analizuojama antros eiles pagal laika ir erdve monotonine “Cabaret” schema. Pateikti testu rezultatai.

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14

Zhdanov, Michael S., Vladimir I. Dmitriev, Sheng Fang, and Gábor Hursán. "Quasi‐analytical approximations and series in electromagnetic modeling." GEOPHYSICS 65, no. 6 (November 2000): 1746–57. http://dx.doi.org/10.1190/1.1444859.

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The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi‐analytical method using iterations and develop higher order approximations resulting in quasi‐analytical series which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, which insures rapid convergence to the correct result. Numerical studies demonstrate that quasi‐analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.

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15

Malyshev, Igor. "On some perturbation techniques for quasi-linear parabolic equations." Journal of Applied Mathematics and Stochastic Analysis 3, no. 3 (January 1, 1990): 169–75. http://dx.doi.org/10.1155/s1048953390000168.

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We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in explicit form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

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16

Qaraad, Belgees, Osama Moaaz, Shyam Sundar Santra, Samad Noeiaghdam, Denis Sidorov, and Elmetwally M. Elabbasy. "Oscillatory Behavior of Third-Order Quasi-Linear Neutral Differential Equations." Axioms 10, no. 4 (December 17, 2021): 346. http://dx.doi.org/10.3390/axioms10040346.

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In this paper, we consider a class of quasilinear third-order differential equations with a delay argument. We establish some conditions of such certain third-order quasi-linear neutral differential equation as oscillatory or almost oscillatory. Those criteria improve, complement and simplify a number of existing results in the literature. Some examples are given to illustrate the importance of our results.

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17

Zhang, Shenggang, Chungang Zhu, and Qinjiao Gao. "Numerical Solution of High-Dimensional Shockwave Equations by Bivariate Multi-Quadric Quasi-Interpolation." Mathematics 7, no. 8 (August 12, 2019): 734. http://dx.doi.org/10.3390/math7080734.

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Radial basis function-based quasi-interpolation performs efficiently in high-dimensional approximation and its applications, which can attain the approximant and its derivatives directly without solving any large-scale linear system. In this paper, the bivariate multi-quadrics (MQ) quasi-interpolation is used to simulate two-dimensional (2-D) Burgers’ equation. Specifically, the spatial derivatives are approximated by using the quasi-interpolation, and the time derivatives are approximated by forward finite difference method. One advantage of the proposed scheme is its simplicity and easy implementation. More importantly, the proposed scheme opens the gate to meshless adaptive moving knots methods for the high-dimensional partial differential equations (PDEs) with shock or soliton waves. The scheme is also applicable to other non-linear high-dimensional PDEs. Two numerical examples of Burgers’ equation (shock wave equation) and one example of the Sine–Gordon equation (soliton wave equation) are presented to verify the high accuracy and efficiency of this method.

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18

Carbonaro, P. "Exceptional hyperbolic systems of Hamiltonian form." European Journal of Applied Mathematics 6, no. 2 (April 1995): 157–67. http://dx.doi.org/10.1017/s0956792500001753.

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Some years ago, Bluman [1] gave the ‘integrability conditions’ for a linear second-order hyperbolic Equation, i.e. the conditions under which it can be mapped invertibly to a constant coefficient wave equation. Considering that a second-order hyperbolic equation in two dimensions can be regarded as the hodograph representation of a 2x2 quasi-linear homogeneous system, one may wonder how the fulfilment of the above-mentioned integrability conditions is reflected in the structure of the quasi-linear system. The question is especially interesting if the quasi-linear system derives from a Hamiltonian density.

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19

Brozos-Vázquez, Miguel, Eduardo García-Río, Peter Gilkey, and Xabier Valle-Regueiro. "A natural linear equation in affine geometry: The affine quasi-Einstein Equation." Proceedings of the American Mathematical Society 146, no. 8 (May 4, 2018): 3485–97. http://dx.doi.org/10.1090/proc/14090.

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20

BRIHAYE, Y., and PIOTR KOSINSKI. "QUASI-EXACTLY SOLVABLE RADIAL DIRAC EQUATIONS." Modern Physics Letters A 13, no. 18 (June 14, 1998): 1445–52. http://dx.doi.org/10.1142/s0217732398001522.

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In the background of a central Coulomb potential, the Schrödinger and Dirac equations lead to exactly solvable spectral problems. When the Schrödinger–Coulomb equation is supplemented by a Harmonic potential, the corresponding spectral problem still possesses a finite number of algebraic solutions: it is quasi-exactly solvable. In this letter we analyze the spectral problem corresponding to the Dirac–Coulomb problem supplemented by a linear radial potential and we show that it also leads to quasi-exactly solvable equations.

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21

Kuznetsov, Ivan, and Sergey Sazhenkov. "Singular limits of the quasi-linear Kolmogorov-type equation with a source term." Journal of Hyperbolic Differential Equations 18, no. 04 (December 2021): 789–856. http://dx.doi.org/10.1142/s0219891621500247.

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Existence, uniqueness and stability of kinetic and entropy solutions to the boundary value problem associated with the Kolmogorov-type, genuinely nonlinear, degenerate hyperbolic–parabolic (ultra-parabolic) equation with a smooth source term is established. In addition, we consider the case when the source term contains a small positive parameter and collapses to the Dirac delta-function, as this parameter tends to zero. In this case, the limiting passage from the original equation with the smooth source to the impulsive ultra-parabolic equation is investigated and the formal limit is rigorously justified. Our proofs rely on the use of kinetic equations and the compensated compactness method for genuinely nonlinear balance laws.

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22

Kohler, Simon, and Wolfgang Reichel. "Breather solutions for a quasi‐linear ‐dimensional wave equation." Studies in Applied Mathematics 148, no. 2 (October 11, 2021): 689–714. http://dx.doi.org/10.1111/sapm.12455.

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23

Lyubanova, Anna Sh. "On an Inverse Problem for Quasi-Linear Elliptic Equation." Journal of Siberian Federal University. Mathematics & Physics 8, no. 1 (February 2015): 38–48. http://dx.doi.org/10.17516/1997-1397-2015-8-1-38-48.

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24

Takeuchi, Yoshiyuki. "Quasi-State Equation of Linear Systems with Time Delay." IEEJ Transactions on Electronics, Information and Systems 112, no. 4 (1992): 270–71. http://dx.doi.org/10.1541/ieejeiss1987.112.4_270.

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25

Donati-Martin, Catherine. "Quasi-Linear Elliptic Stochastic Partial Differential Equation: Markov property." Stochastics and Stochastic Reports 41, no. 4 (December 1992): 219–40. http://dx.doi.org/10.1080/17442509208833804.

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26

Rosenau, Philip. "Compact breathers in a quasi-linear Klein–Gordon equation." Physics Letters A 374, no. 15-16 (April 2010): 1663–67. http://dx.doi.org/10.1016/j.physleta.2010.01.065.

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27

Esposito, Pierpaolo. "A classification result for the quasi-linear Liouville equation." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 3 (May 2018): 781–801. http://dx.doi.org/10.1016/j.anihpc.2017.08.002.

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28

Ghosh, Tuhin, and Karthik Iyer. "Cloaking for a quasi-linear elliptic partial differential equation." Inverse Problems & Imaging 12, no. 2 (2018): 461–91. http://dx.doi.org/10.3934/ipi.2018020.

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29

Kapaev, A. A. "Quasi-linear Stokes phenomenon for the Painlevé first equation." Journal of Physics A: Mathematical and General 37, no. 46 (November 4, 2004): 11149–67. http://dx.doi.org/10.1088/0305-4470/37/46/005.

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30

Squassina, Marco. "Boundary behavior for a singular quasi-linear elliptic equation." Journal of Mathematical Analysis and Applications 393, no. 2 (September 2012): 692–96. http://dx.doi.org/10.1016/j.jmaa.2012.04.023.

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31

Belan, E. P. "Quasi-periodic solutions of a linear functional-differential equation." Journal of Mathematical Sciences 82, no. 3 (November 1996): 3416–19. http://dx.doi.org/10.1007/bf02362656.

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32

Ravasoo, Arvi. "Modified constitutive equation for quasi-linear theory of viscoelasticity." Journal of Engineering Mathematics 78, no. 1 (April 27, 2011): 111–18. http://dx.doi.org/10.1007/s10665-011-9473-5.

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33

Selvaratnam, A. R., M. Vlieg-Hulstman, B. van-Brunt, and W. D. Halford. "On the solution of a class of second-order quasi-linear PDEs and the Gauss equation." ANZIAM Journal 42, no. 3 (January 2001): 312–23. http://dx.doi.org/10.1017/s1446181100011962.

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AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain classes of non-linear second order PDEs of hyperbolic type by identifying these PDEs as the Gauss equation in some coördinate system. The possibility of solving the Cauchy Problem has also been explored for these classes of equations.

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34

Wan, Renhui. "Long time stability for the dispersive SQG equation and Boussinesq equations in Sobolev space Hs." Communications in Contemporary Mathematics 22, no. 03 (September 10, 2018): 1850063. http://dx.doi.org/10.1142/s0219199718500633.

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Dispersive SQG equation have been studied by many works (see, e.g., [M. Cannone, C. Miao and L. Xue, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, Proc. Londen. Math. Soc. 106 (2013) 650–674; T. M. Elgindi and K. Widmayer, Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems, SIAM J. Math. Anal. 47 (2015) 4672–4684; A. Kiselev and F. Nazarov, Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation, Nonlinearity 23 (2010) 549–554; R. Wan and J. Chen, Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations, Z. Angew. Math. Phys. 67 (2016) 104]), which is very similar to the 3D rotating Euler or Navier–Stokes equations. Long time stability for the dispersive SQG equation without dissipation was obtained by Elgindi–Widmayer [Sharp decay estimates for an anisotropic linear semigroup and applications to the surface quasi-geostrophic and inviscid Boussinesq systems, SIAM J. Math. Anal. 47 (2015) 4672–4684], where the initial condition [Formula: see text] [Formula: see text] plays a important role in their proof. In this paper, by using the Strichartz estimate, we can remove this initial condition. Namely, we only assume the initial data is in the Sobolev space like [Formula: see text]. As an application, we can also obtain similar result for the 2D Boussinesq equations with the initial data near a nontrivial equilibrium.

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35

Cisneros-Ake, Luis A. "Quasi-steady state propagation in the davydov-type model with linear on-site interactions." Low Temperature Physics 48, no. 12 (December 2022): 1015–21. http://dx.doi.org/10.1063/10.0015110.

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The problem of electron transportation along a discrete deformable medium with linear on-site interactions in the Davydov approach is considered. It is found that the quasi-stationary state of the full equations of motion leads to a discrete nonlocal nonlinear Schrödinger (DNNLS) equation whose nonlocality is of the exponential type and depending on the on-site parameter. We use the variational approach to approximate discrete traveling wave solutions in the DNNLS equation. We find that the discrete solutions continued from the discrete nonlinear Schrödinger equation, corresponding to the vanishing of the on-site parameter, bifurcates in a critical on-site value. Additionally, a threshold in the velocity of propagation of the discrete structures is found.

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36

Astashova, I. V. "ON OSCILLATION OF SOLUTIONS TO QUASI-LINEAR EMDEN – FOWLER TYPE HIGHER-ORDER DIFFERENTIAL EQUATIONS." Vestnik of Samara University. Natural Science Series 21, no. 6 (May 17, 2017): 12–22. http://dx.doi.org/10.18287/2541-7525-2015-21-6-12-22.

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Existence and behavior of oscillatory solutions to nonlinear equations with regular and singular power nonlinearity are investigated. In particular, the existence of oscillatory solutions is proved for the equation y(n) + P(x; y; y ′ ; : : : ; y(n−1))|y|k sign y = 0; n 2; k ∈ R; k 1; P ̸= 0; P ∈ C(Rn+1): A criterion is formulated for oscillation of all solutions to the quasilinear even-order differential equation y(n) + nΣ−1 i=0 aj(x) y(i) + p(x) |y|ksigny = 0; p ∈ C(R); aj ∈ C(R); j = 0; : : : ; n − 1; k 1; n = 2m; m ∈ N; which generalizes the well-known Atkinson’s and Kiguradze’s criteria. The existence of quasi-periodic solutions is proved both for regular (k 1) and singular (0 k 1) nonlinear equations y(n) + p0 |y|ksigny = 0; n 2; k ∈ R; k 0; k ̸= 1; p0 ∈ R; with (−1)np0 0: A result on the existence of periodic oscillatory solutions is formulated for this equation with n = 4; k 0; k ̸= 1; p0 0:

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37

Mohammad, Mutaz. "A Numerical Solution of Fredholm Integral Equations of the Second Kind Based on Tight Framelets Generated by the Oblique Extension Principle." Symmetry 11, no. 7 (July 2, 2019): 854. http://dx.doi.org/10.3390/sym11070854.

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In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate.

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Jiao, Xiarong, Shan Jiang, and Hong Liu. "Nonlinear Moving Boundary Model of Low-Permeability Reservoir." Energies 14, no. 24 (December 14, 2021): 8445. http://dx.doi.org/10.3390/en14248445.

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At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant pressure outer boundary and closed outer boundary are compared with the analytical solutions. The calculation results show that it is reliable to solve the oil-gas seepage equation with the moving boundary nonlinear equation. To deal with the difficulty in solving analytical solutions for low-permeability reservoirs and numerical solutions of moving boundaries, a quasi-linear model and a nonlinear moving boundary model were proposed based on the characteristics of low-permeability reservoirs. The production decline curve chart of the quasi-linear model and the recovery factor calculation chart were drawn, and the sweep radius calculation formula was also established. The research results can provide a theoretical reference for the policy-making of development technology in low-permeability reservoirs.

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Huang, Chen. "A variant of Clark’s theorem and its applications for nonsmooth functionals without the global symmetric condition." Advances in Nonlinear Analysis 11, no. 1 (July 29, 2021): 285–303. http://dx.doi.org/10.1515/anona-2020-0197.

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Abstract We give a new non-smooth Clark’s theorem without the global symmetric condition. The theorem can be applied to generalized quasi-linear elliptic equations with small continous perturbations. Our results improve the abstract results about a semi-linear elliptic equation in Kajikiya [10] and Li-Liu [11].

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Feldman, Richard M., Bryan L. Deuermeyer, and Ciriaco Valdez-Flores. "Utilization of the method of linear matrix equations to solve a quasi-birth-death problem." Journal of Applied Probability 30, no. 3 (September 1993): 639–49. http://dx.doi.org/10.2307/3214772.

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The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a vehicle to compare the two approaches for solving quasi-birth-death processes.

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Feldman, Richard M., Bryan L. Deuermeyer, and Ciriaco Valdez-Flores. "Utilization of the method of linear matrix equations to solve a quasi-birth-death problem." Journal of Applied Probability 30, no. 03 (September 1993): 639–49. http://dx.doi.org/10.1017/s0021900200044375.

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The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a vehicle to compare the two approaches for solving quasi-birth-death processes.

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Yermachenko, I., and F. Sadyrbaev. "QUASILINEARIZATION AND MULTIPLE SOLUTIONS OF THE EMDEN‐FOWLER TYPE EQUATION." Mathematical Modelling and Analysis 12, no. 1 (March 31, 2005): 41–50. http://dx.doi.org/10.3846/13926292.2005.9637269.

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Existence and multiplicity of solutions of the problem x” = ‐q(t) |x|p sign x (i), x(0) = x(1) = 0 (ii) are investigated by reducing equation (i) to a quasi‐linear one so that both equations are equivalent in some domain O. If a solution of corresponding quasi‐linear problem is located in the domain of equivalence O, then this solution solves the original problem also. If this process of quasilinearization is possible for multiple essentially different linear parts, then multiple solutions to the problem (i), (ii) exist. Darbe nagrinejamas taip vadinamas Emdeno‐Faulerio kvazitiesines diferencialines lygties homogeninio kraštinio uždavinio sprendiniu egzistavimas ir daugialypumas. Parodyta, kad šio uždavinio sprendinio daugialypumas priklauso nuo tam tikru būdu gautos kvazilinearizuotos lygties tiesines dalies savybiu.

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Ghosh, Bishnu Pada, and Nepal Chandra Roy. "Numerical Method for 2D Quasi-linear Hyperbolic Equation on an Irrational Domain: Application to Telegraphic Equation." Dhaka University Journal of Science 69, no. 2 (December 1, 2021): 116–23. http://dx.doi.org/10.3329/dujs.v69i2.56492.

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We develop a novel three-level compact method (implicit) of second order in time and space directions using unequal grid for the numerical solution of 2D quasi-linear hyperbolic partial differential equations on an irrational domain. The stability analysis of the model problem for unequal mesh is discussed and it is revealed that the developed scheme is unconditionally stable for the Telegraphic equation. For linear difference equations on an irrational domain, the alternating direction implicit method is discussed. The projected technique is scrutinized on several physical problems on an irrational domain to exhibitthe accuracy and effectiveness of the suggested method. Dhaka Univ. J. Sci. 69(2): 116-123, 2021 (July)

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Perepelkin, E. E., and E. P. Zhidkov. "An Analytical Approach for Quasi-Linear Equation in Second Order." Computational Methods in Applied Mathematics 1, no. 3 (2001): 285–97. http://dx.doi.org/10.2478/cmam-2001-0019.

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AbstractThis paper is devoted to the studies of the properties of the solutions of non-linear partial differential equation, being basic ones in differential formulation of the magnetostatic problem of finding the magnetic field dis- tribution. The question of the existence of solutions, possessing an unlimited gradient, for this equation is of particular interest. Previous works dealt with the linear equation type, and also a boundary value problem was con- sidered for certain requirements for the µ function, as well as a more general non-linear case was studied. It was shown that such solutions exist, and their properties will be investigated. The difference scheme for the boundary value problem was built in the domain with corner and numerical calculations were given.

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Izadi, Mohammad, Şuayip Yüzbaşi, and Samad Noeiaghdam. "Approximating Solutions of Non-Linear Troesch’s Problem via an Efficient Quasi-Linearization Bessel Approach." Mathematics 9, no. 16 (August 4, 2021): 1841. http://dx.doi.org/10.3390/math9161841.

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Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving the non-linear Troesch’s problem. In the first approach, by expressing the unknown solution and its second derivative in terms of the Bessel matrix form along with some collocation points, the governing equation transforms into a non-linear algebraic matrix equation. In the second approach, the technique of quasi-linearization is first employed to linearize the model problem and, then, the first collocation method is applied to the sequence of linearized equations iteratively. In the latter approach, we require to solve a linear algebraic matrix equation in each iteration. Moreover, the error analysis of the Bessel series solution is established. In the end, numerical simulations and computational results are provided to illustrate the utility and applicability of the presented collocation approaches. Numerical comparisons with some existing available methods are performed to validate our results.

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Makarov, V. L., and L. I. Demkiv. "Accuracy Estimates of Difference Schemes for Quasi-linear Parabolic Equations Taking into Account the Initial-boundary Effect." Computational Methods in Applied Mathematics 3, no. 4 (2003): 579–95. http://dx.doi.org/10.2478/cmam-2003-0036.

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AbstractFor difference schemes the initial-boundary problem for quasi-linear parabolic-type equations, ’a priori weight estimates’ of the error have been found. These estimates show how much the accuracy of difference schemes near the boundary of a time rectangle is higher than in the middle of it. Sufficient conditions of smoothness of the coefficients and the right-hand side of the quasi-linear parabolic equation and the initial conditions have been found. These conditions ensure a correctness of these a priori estimates.

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Sang, Yanbin, and Xiaorong Luo. "On quasi-linear equation problems involving critical and singular nonlinearities." Journal of Nonlinear Sciences and Applications 10, no. 09 (September 23, 2017): 4966–82. http://dx.doi.org/10.22436/jnsa.010.09.36.

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Boufoussi, Brahim, and Salah Hajji. "An approximation result for a quasi-linear stochastic heat equation." Statistics & Probability Letters 80, no. 17-18 (September 2010): 1369–77. http://dx.doi.org/10.1016/j.spl.2010.05.001.

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Chabrowski, J. H. "On the Dirichlet problem for a quasi-linear elliptic equation." Rendiconti del Circolo Matematico di Palermo 35, no. 1 (January 1986): 159–68. http://dx.doi.org/10.1007/bf02844049.

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Zheng, Shenzhou, and Xiuying Kang. "THE COMPARISON OF GREEN FUNCTION FOR QUASI-LINEAR ELLIPTIC EQUATION." Acta Mathematica Scientia 25, no. 3 (July 2005): 470–80. http://dx.doi.org/10.1016/s0252-9602(05)60010-0.

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