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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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Dates and versions

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

Identifiers

  • HAL Id : hal-01643317 , version 1

Cite

María Anguiano. Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media. 2017. ⟨hal-01643317v1⟩
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