Existência de soluções estacionárias estáveis para equações de reação-difusão com condição de fronteira de Neumann não-linear: condições necessárias e condições suficientes.

Abstract

In this work we consider some nonlinear reaction-difusion equations with nonlinear Neumann boundary condition. The objective is to present conditions on the geometry of the domain, as well as on the reaction and diffusion terms, for the existence of stationary stable nonconstant solutions which develop internal and superficial transition layers. The main tools used are Gamma-convergence of functionals, variational techniques and results of dynamical systems in infinite dimension.