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

María Anguiano (1)

1 Universidad de Sevilla = University of Seville

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.

Mots clés: 35K57 Keywords: Homogenization; dynamical boundary conditions; perforated media

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

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