Stable Multiple-layer Stationary Solutions of a Semilinear Parabolic Equation in Two-dimensional Domains

Abstract

We use Γ-convergence to prove existence of stable multiple-layer stationary solutions (stable patterns) to a reaction-diffusion equation. Given nested simple closed curves in R2, we give sufficient conditions on their curvature so that the reaction-diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.