pp. 73{78 THE BOUNDEDNESS OF PROPAGATION SPEEDS OF DISTURBANCES FOR REACTION-DIFFUSION SYSTEMS

Abstract. It is shown that propagation speeds of disturbances are bounded for a class of reaction-diusion systems. It turns out that solutions for various initial states are conned by traveling waves. A new technique is presented for the construction of the comparison functions. The technique is based on the operator-splitting methodology, which is known as a numerical computation method. By using an exact solution of the Fisher equation we can make a simple proof. In this paper the outline of the proof is given. Key words. reaction-diusion system, comparison technique, operator-splitting method, trav-eling wave AMS subject classications. 35B05, 35K45, 35K57 1. Introduction. W