Rotating Spiral Wave Solutions of Reaction-Diffusion Equations

We resolve the question of existence of regular rotating spiral waves as a consequence of only the processes of chemical reaction and molecular diffusion. We prove rigorously the existence of these waves as solutions of reaction-diffusion equations, and we exhibit them by means of numerical computations in several concrete cases. Existence is proved via the Schauder fixed point theorem applied to a class of functions with sufficient structure that, in fact, important constructive properties such as asymptotic representations and frequency of rotation are obtained.