On convergence and compactness in parabolic problems with globally large diffusion and nonlinear boundary conditions

Abstract

We establish some abstract convergence and compactness results for families of singularly perturbed semilinear parabolic equations and apply them to reaction-diffusion equations with nonlinear boundary conditions and large diffusion. This refines some previous results of [R. Willie, < i> A semilinear reaction-diffusion system of equations and large diffusion< /i> , J. Dynam. Differential Equations < b> 16< /b> (2004), 35-63].