We consider the evolution of the solution of a class of scalar nonlinear hyperbolic reaction–diffusion equations which incorporate a relaxation time and with a reaction function given by a monostable cubic polynomial. An initial-value problem is studied when the prescribed starting data are given by a simple step function. It is established that the large-time structure of the solution is governed by the evolution of a propagating wave-front. The character of this front can be one of three forms, either reaction–diffusion, reaction–relaxation or reaction–relaxation–diffusion, which is relevant and depends on the particular values of the problem parameters that describe the underlying reaction polynomial.
History
Publication title
Journal of Engineering Mathematics
Volume
130
ISSN
0022-0833
Department/School
School of Natural Sciences
Publisher
Kluwer Academic Publ
Place of publication
Van Godewijckstraat 30, Dordrecht, Netherlands, 3311 Gz