Abstract
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.
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Acknowledgements
The authors are indebted to the referees and Associate Editor Thomas Witelski who made several very helpful suggestions for substantial improvements to the paper and pointed out a number of significant references of which we were previously unaware.
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Leach, J.A., Bassom, A.P. Large-time solutions of a class of scalar, nonlinear hyperbolic reaction–diffusion equations. J Eng Math 130, 2 (2021). https://doi.org/10.1007/s10665-021-10159-7
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DOI: https://doi.org/10.1007/s10665-021-10159-7