Concentrating patterns of reaction-diffusion systems: A variational approach

Ding, Yanheng; Xu, Tian

doi:10.1090/tran/6626

Concentrating patterns of reaction-diffusion systems: A variational approach
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by Yanheng Ding and Tian Xu PDF

Trans. Amer. Math. Soc. 369 (2017), 97-138 Request permission

Abstract:

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.

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