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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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https://hal.archives-ouvertes.fr/hal-01643317
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Submitted on : Tuesday, November 21, 2017 - 12:46:11 PM
Last modification on : Saturday, June 19, 2021 - 12:44:39 PM

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  • HAL Id : hal-01643317, version 1

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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, Springer Verlag, 2020. ⟨hal-01643317⟩

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