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Journal Articles Mediterranean Journal of Mathematics Year : 2020

Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media

Abstract

We consider a nonlinear parabolic problem with dynamical boundary conditions in a media perforated by periodically distributed holes of size ε. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when ε goes to zero, a new nonlinear parabolic problem defined on a unified domain without holes with zero Dirichlet boundary condition and with extra-terms coming from the influence of the dynamical boundary conditions is rigorously derived.
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Dates and versions

hal-01643317 , version 1 (21-11-2017)
hal-01643317 , version 2 (16-01-2024)

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María Anguiano. Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media. Mediterranean Journal of Mathematics, 2020, 17 (18), ⟨10.1007/s00009-019-1459-y⟩. ⟨hal-01643317v2⟩

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