Stability of a class of nonlinear reaction–diffusion equations and stochastic homogenization

We establish a convergence theorem for a class of nonlinear reaction–diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of functionals of the calculus of variations equipped with the Mosco-convergence. The reaction term, which is not globally Lipschi...

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Bibliographic Details
Published in:Asymptotic analysis 2019-01, Vol.115 (3-4), p.169-221
Main Authors: Anza Hafsa, Omar, Mandallena, Jean Philippe, Michaille, Gérard
Format: Article
Language:English
Subjects:
Analysis of PDEs
Calculus of variations
Classical Analysis and ODEs
Convergence
Diffusion
Homogenization
Mathematics
Nonlinear equations
Reaction-diffusion equations
State variable
Theorems
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Summary:We establish a convergence theorem for a class of nonlinear reaction–diffusion equations when the diffusion term is the subdifferential of a convex functional in a class of functionals of the calculus of variations equipped with the Mosco-convergence. The reaction term, which is not globally Lipschitz with respect to the state variable, gives rise to bounded solutions, and cover a wide variety of models. As a consequence we prove a homogenization theorem for this class under a stochastic homogenization framework.
ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-191531