Positive Solutions of a Nonlinear Parabolic Partial Differential Equation [PDF]
Abstract and Applied Analysis, 2014 We deal with the existence and uniqueness of positive solutions to a class of nonlinear parabolic partial differential equations, by using some fixed point theorems for mixed monotone operators with perturbation.
Chengbo Zhai, Shunyong Li
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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
Gabriel J. Lord, Tony Shardlow
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Minimal solutions to a class of parabolic partial differential equations [PDF]
Proceedings of the American Mathematical Society, 1969 2. Statement of the problem. Let T be a closed interval [to, t'] of the real line. Suppose Q is an open set in n-dimensional Euclidean space En and let i2 be a compact subset of R. Let 9j be the set of real-valued functions u(t, x) defined on TXQ and absolutely continuous on T for almost all x such that for some fixed integer k, the function u and all ...
T. Guinn, Edward M. Landesman
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Parabolic and pseudo-parabolic partial differential equations* [PDF]
Journal of the Mathematical Society of Japan, 1969 Tsuan Wu Ting
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Intermittence and nonlinear parabolic stochastic partial differential equations
Electronic Journal of Probability, 2008 We consider nonlinear parabolic SPDEs of the form $\partial_t u=\sL u + (u)\dot w$, where $\dot w$ denotes space-time white noise, $ :\R\to\R$ is [globally] Lipschitz continuous, and $\sL$ is the $L^2$-generator of a L vy process. We present precise criteria for existence as well as uniqueness of solutions.
Mohammud Foondun, Davar Khoshnevisan
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Elementary Solutions for Certain Parabolic Partial Differential Equations [PDF]
Transactions of the American Mathematical Society, 1956 H. P. McKean
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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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Solving linear parabolic rough partial differential equations [PDF]
Journal of Mathematical Analysis and Applications, 2020 We study linear rough partial differential equations in the setting of [Friz and Hairer, Springer, 2014, Chapter 12]. More precisely, we consider a linear parabolic partial differential equation driven by a deterministic rough path W of Hölder regularity with .
John Schoenmakers +5 more
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