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

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 $\epsilon$. 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 $\epsilon$ 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.

20 pages

References in corpus (1)

• Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

Cited by in corpus (1)

• A nonlocal memory strange term arising in the critical scale homogenisation of a diffusion equation with a dynamic boundary condition