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

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of engineering mathematics 2021-10, Vol.130 (1), Article 2
Main Authors: Leach, J. A., Bassom, Andrew P.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Diffusion
Evolution
Mathematical analysis
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Polynomials
Reaction-diffusion equations
Relaxation time
Step functions
Theoretical and Applied Mechanics
Wave fronts
Wave propagation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-021-10159-7