Stability of Single Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity

Abstract: Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using the analytical singular perturbation theory. Moreover, a stability criterion for the stationary solutions is provided by calculating the Evans function.