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arXiv · 1712.01183

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

María Anguiano
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Abstract

We consider a nonlinear parabolic problem with nonlinear dynamical boundary conditions of pure-reactive type in a media perforated by periodically distributed holes of size $\varepsilon$. The novelty of our work is to consider a nonlinear model where the nonlinearity also appears in the boundary. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when $\varepsilon$ 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 nonlinear dynamical boundary conditions is rigorously derived.

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María Anguiano. 2017-12-04. Existence, uniqueness and homogenization of nonlinear parabolic problems with dynamical boundary conditions in perforated media. https://doi.org/10.1007/s00009-019-1459-y

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