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Existence, Uniqueness and Homogenization of Nonlinear Parabolic Problems with Dynamical Boundary Conditions in Perforated Media

  • María AnguianoEmail author
Article
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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.

Keywords

Homogenization perforated media dynamical boundary conditions 

Mathematics Subject Classification

Primary 35B27 Secondary 35K57 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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