CONCENTRATING PATTERNS OF REACTION-DIFFUSION SYSTEMS: A VARIATIONAL APPROACH

Our purpose is to motivate an analytic characterization aimed at predicting patterns for general reaction-diffusion systems, depending on the spatial distribution involved in the reaction terms. It is shown that there must be a pattern concentrating around the local minimum of the chemical potential distribution for small diffusion coefficients. A multiple concentrating result is also established to illustrate the mechanisms leading to emergent spatial patterns. The results of this paper were proved by using a general variational technique. This enables us to consider nonlinearities which grow either super quadratic or asymptotic quadratic at infinity.