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


Leach, JA and Bassom, AP, Large-time solutions of a class of scalar, nonlinear hyperbolic reaction-diffusion equations, Journal of Engineering Mathematics, 130 Article 2. ISSN 0022-0833 (2021) [Refereed Article]

DOI: doi:10.1007/s10665-021-10159-7


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 Details

Item Type:Refereed Article
Keywords:asymptotic solutions, monostable cubic reaction, monostable cubic reaction term, reaction–diffusion equations
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Approximation theory and asymptotic methods
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:147872
Year Published:2021
Deposited By:Mathematics
Deposited On:2021-11-19
Last Modified:2022-05-20

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