A stability analysis for a semilinear parabolic partial differential equation [PDF]
Journal of Differential Equations, 1974 AbstractWe consider a parabolic partial differential equation ut = uxx + f(u), where − ∞ < x < + ∞ and 0 < t < + ∞. Under suitable hypotheses pertaining to f, we exhibit a class of initial data φ(x), − ∞ < x < + ∞, for which the corresponding solutions u(x, t) approach zero as t → + ∞.
N. Chafee
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Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation [PDF]
SIAM Journal on Numerical Analysis, 1968 G. Fichera [1] and other authors have investigated partial differential equations of the form [Eq. 1.1] in which the matrix (aij(x)) is required to be semidefinite. Equations of this type occur in the theory of random processes. A numerical analysis of some equations of this type has been by Cannon and Hill [9].
J. Franklin, E. Rodemich
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Bifurcation and stability for a nonlinear parabolic partial differential equation [PDF]
Bulletin of the American Mathematical Society, 1974 Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
N. Chafee, E. Infante
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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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On the solution of parabolic partial differential equations in Chebyshev series [PDF]
The Computer Journal, 1971 D. Knibb
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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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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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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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