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Homogenization of parabolic problems with dynamical boundary conditions of reactive-diffusive type in perforated media

Abstract : This paper deals with the homogenization of the reaction-diffusion equations in a domain containing periodically distributed holes of size ε, with a dynamical boundary condition of reactive-diffusive type, i.e., we consider the following nonlinear boundary condition on the surface of the holes ∇uε · ν + ε ∂uε ∂t = ε δ∆Γuε − ε g(uε), where ∆Γ denotes the Laplace-Beltrami operator on the surface of the holes, ν is the outward normal to the boundary, δ > 0 plays the role of a surface diffusion coefficient and g is the nonlinear term. We generalize our previous results (see [3]) established in the case of a dynamical boundary condition of pure-reactive type, i.e., with δ = 0. We prove the convergence of the homogenization process to a nonlinear reaction-diffusion equation whose diffusion matrix takes into account the reactive-diffusive condition on the surface of the holes.
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Submitted on : Friday, June 5, 2020 - 1:04:41 PM
Last modification on : Saturday, June 19, 2021 - 12:50:34 PM

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María Anguiano. Homogenization of parabolic problems with dynamical boundary conditions of reactive-diffusive type in perforated media. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2020. ⟨hal-02394935v2⟩

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