Results 1 to 10 of about 100,034 (331)
Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques.
G. Adomian
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Normal forms for parabolic partial differential equations
, 1993 Summary: The authors begin a study of normal form theorems for parabolic partial differential equations \[ \partial_ t v= \partial_ x^ 2 v+\mu v-v^ 3- \varepsilon R(v), \] where \(R\) is a polynomial whose terms are all of degree 4 or higher. They show that despite the presence of resonances one can construct a partial normal form for perturbations of ...
Jean‐Pierre Eckmann +2 more
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Quasilinear Parabolic Equations Associated with Semilinear Parabolic Equations
Mathematics, 2023 We formulate a quasilinear parabolic equation describing the behavior of the global-in-time solution to a semilinear parabolic equation. We study this equation in accordance with the blow-up and quenching patterns of the solution to the original ...
Katsuyuki Ishii +2 more
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On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula
Mathematics, 2023 The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics.
Byoung Seon Choi, Moo Young Choi
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Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise
Nonlinear Analysis, 2021 The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for
Gregory Amali Paul Rose +2 more
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Markov processes and parabolic partial differential equations
, 2010 In the first part of this article, we present the main tools and definitions of Markov processes' theory: transition semigroups, Feller processes, infinitesimal generator, Kolmogorov's backward and forward equations and Feller diffusion. We also give several classical examples including stochastic differential equations (SDEs) and backward SDEs (BSDEs).
Mireille Bossy, Nicolas Champagnat
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Two approximation methods for fractional order Pseudo-Parabolic differential equations
Alexandria Engineering Journal, 2022 In this study, fractional order pseudo-parabolic partial differential equation defined by Caputo derivative is investigated with initial-boundary conditions. Modified double Laplace decomposition method is used to find the exact solution of this equation.
Mahmut. Modanli +4 more
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Postprocessing for Stochastic Parabolic Partial Differential Equations [PDF]
SIAM Journal on Numerical Analysis, 2007 We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce postprocessing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [G. J. Lord and J. Rougemont, IMA J. Numer. Anal., 24 (2004), pp. 587-604] and use an
Shardlow, Tony, Lord, Gabriel
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A priori estimate of the solution of the Cauchy problem in the Sobolev classes for discontinuous coefficients of degenerate heat equations [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 Partial differential equations of the parabolic type with discontinuous coefficients and the heat equation degenerating in time, each separately, have been well studied by many authors.
U.K. Koilyshov +2 more
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Boundary Value Problems, 2018 This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We prove that the function given by the solution of
Ning Ma, Zhen Wu
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