Locally Stable Dynamics for Reaction Diffusion Systems

Abstract

We shall be concerned with the dynamics of solutions to systems of reaction diffusion equations. To be more precise we consider a weakly coupled semilinear parabolic system of the form:

$$ \partial u/\partial t = D\Delta u + f\left( u \right){\text{ }}x \in \Omega ,t > 0 $$

(1.1a)

$$ \partial u/\partial n = 0{\text{ }}x \in \partial \Omega ,t > 0 $$

(1.1b)

$$ u\left( {x,0} \right) = {u_0}\left( x \right){\text{ }}x \in \Omega $$

(1.1c)

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These authors gratefully acknowledge the support of NSF Grants DMS 9207064 and DMS 9208046 respectively.