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Large-time solutions of a class of scalar, nonlinear hyperbolic reaction–diffusion equations

Leach, JA and Bassom, AP ORCID: 0000-0003-3275-7801 2021 , 'Large-time solutions of a class of scalar, nonlinear hyperbolic reaction–diffusion equations' , Journal of Engineering Mathematics, vol. 130 , doi: 10.1007/s10665-021-10159-7.

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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.

Item Type: Article
Authors/Creators:Leach, JA and Bassom, AP
Keywords: asymptotic solutions, monostable cubic reaction, monostable cubic reaction term, reaction–diffusion equations
Journal or Publication Title: Journal of Engineering Mathematics
Publisher: Kluwer Academic Publ
ISSN: 0022-0833
DOI / ID Number: 10.1007/s10665-021-10159-7
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