Ulam-Hyers stability of a parabolic partial differential equation
Demonstratio Mathematica, 2019 The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability.
Marian Daniela +2 more
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On a parabolic partial differential equation and system modeling a production planning problem
Electronic Research Archive, 2022 We consider a parabolic partial differential equation and system derived from a production planning problem dependent on time. Our goal is to find a closed-form solution for the problem considered in our model.
Dragos-Patru Covei
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Homogenization of a nonlinear random parabolic partial differential equation
Stochastic Processes and their Applications, 2003 The homogenization problem for a semilinear second order parabolic equation with random coefficients \[ \partial _ {t}u^ \varepsilon = \sum ^ {n}_ {i,j=1}\partial _ {x_ {i}}\Bigl (a_ {ij}\Bigl (\frac {x}{\varepsilon }, \xi _ {t/\varepsilon ^ 2}\Bigr )\partial _ {x_ {j}} u^ \varepsilon \Bigr ) + \frac 1{\varepsilon }g\Bigl (\frac {x}{\varepsilon }, \xi ...
Pardoux, E., Piatnitski, A.L.
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A model reduction approach to numerical inversion for a parabolic partial differential equation [PDF]
, 2014 We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is ...
Liliana Borcea +3 more
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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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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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Periodic homogenization of a pseudo-parabolic equation via a spatial-temporal decomposition [PDF]
, 2018 Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the Peszyn'ska-Showalter-Yi paper [
AJ Vromans +6 more
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Solving linear parabolic rough partial differential equations [PDF]
, 2018 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 $\mathbf{W}$ of H ...
Bayer, Christian +4 more
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A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation
Abstract and Applied Analysis, 2015 The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly ...
Wenyuan Liao
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