Abstract
Abstract This article is intended to survey the results about pattern formation in a class of reaction-diffusion systems. The focus is on the phenomenon of multiple existence of stable stationary solutions, which has biologically or physically significant consequences. The mathematical structure and stability of stationary solutions is investigated in a certain parameter space. Especially, σ-local stability and instability theorems for D 1 -sheet are given, and stabilization of D 2 -sheet is proved via two approaches: the spectral method and the singular perturbation-theoretic one.
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