Radially symmetric stationary solutions for a MEMS type reaction–diffusion equation with fringing field

Abstract

Abstract Radially symmetric stationary solutions for a micro-electro-mechanical system (MEMS) type reaction–diffusion equation with fringing field are considered. This equation arises in the study of the MEMS devices. This paper is devoted to the study of the existence of these solutions, information about their shape, and their asymptotic behaviour. These are studied by applying the framework that combines Poincaré type compactification, classical dynamical systems theory, and geometric methods for desingularization of vector fields called the blow-up technique.