The evolution of travelling waves in reaction-diffusion equations with monotone decreasing diffusivity. I. Continuous diffusivity

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Abstract
We examine the effects of a concentration dependent diffusivity on a reaction-diffusion process which has applications in chemical kinetics. The diffusivity is taken as a continuous monotone, a decreasing function of concentration that has compact support, of the form that arises in polymerization processes. We consider piecewise-classical solutions to an initial-boundary value problem. The existence of a family of permanent form travelling wave solutions is established, and the development of the solution of the initial-boundary value problem to the travelling wave of minimum propagation speed is considered. It is shown that an interface will always form in finite time, with its initial propagation speed being unbounded. The interface represents the surface of the expanding polymer matrix.

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