Stability Properties of Solutions to Systems of Reaction-Diffusion Equations

Abstract

This paper primarily treats the stability properties of uniform steady solutions to systems of reaction-diffusion equations subject to Neumann boundary data. The importance of such stability questions for physical problems has been made by Turing, Othmer and Scriven, and others.The three cases of equal positive diffusion coefficients, unequal positive diffusion coefficients and unequal nonnegative diffusion coefficients are investigated. The possible destabilizing effects of unequal diffusion coefficients are clearly indicated. In the case of equal diffusion coefficients we estimate the extent of asymptotic stability. We also briefly treat the case when Neumann data is replaced by Dirichlet data. This latter case has been studied more extensively in the literature.