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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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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.
D. Covei
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A note on exponential Rosenbrock-Euler method for the finite element discretization of a semilinear parabolic partial differential equation [PDF]
Computers and Mathematics with Applications, 2016 In this paper we consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media.
Jean Daniel Mukam, Antoine Tambue
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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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Computers and Mathematics with Applications, 2019 In the present study, a new amendment in Laplace variational iteration method for the solution of fourth-order parabolic partial differential equations with variable coefficients is revealed i.e.
M. Nadeem, Fengquan Li, Hijaz Ahmad
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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.
D. Marian +2 more
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Quasilinear parabolic stochastic partial differential equations: Existence, uniqueness
Stochastic Processes and their Applications, 2017 In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone.
Hofmanová, Martina, Zhang, Tusheng
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Resonance and Quasilinear Parabolic Partial Differential Equations
Journal of Differential Equations, 1993 For a certain quasilinear parabolic equation, the authors prove the existence of a weak periodic solution in an adequate Hilbert space under both resonance and nonresonance conditions. The results are obtained by using a Galerkin-type technique.
Lefton, L.E., Shapiro, V.L.
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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 .
Riedel, Sebastian +4 more
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Degenerate parabolic stochastic partial differential equations: Quasilinear case
The Annals of Probability, 2016 Published at http://dx.doi.org/10.1214/15-AOP1013 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org).
Debussche, Arnaud +2 more
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