THE EVOLUTION OF TRAVELING WAVES IN REACTION-DIFFUSION EQUATIONS WITHMONOTONE DECREASING DIFFUSIVITY .1. CONTINUOUS DIFFUSIVITY

We examine the effects of a concentration dependent diffusivity on a r eaction-diffusion process which has applications in chemical kinetics. The diffusivity is taken as a continuous monotone, a decreasing funct ion of concentration that has compact support, of the form that arises in polymerization processes. We consider piecewise-classical solution s to an initial-boundary value problem. The existence of a family of p ermanent form travelling wave solutions is established: and the develo pment of the solution of the initial-boundary value problem to the tra velling wave of minimum propagation speed is considered. It is shown t hat an interface will always form in finite time, with its initial pro pagation speed being unbounded. The interface represents the surface o f the expanding polymer matrix.