The effects of variable diffusivity on the development of travelling waves in a class of reaction-diffusion equations
- 15 August 1994
- journal article
- Published by The Royal Society in Philosophical Transactions A
- Vol. 348 (1687) , 229-260
- https://doi.org/10.1098/rsta.1994.0090
Abstract
In this paper we examine the effects of concentration dependent diffusivity on a reaction-diffusion process which has applications in chemical kinetics and ecology. We consider piecewise classical solutions to an initial boundary-value problem. The existence of a family of permanent form travelling wave solutions is established and the development of the solution of the initial boundary-value problem to the travelling wave of minimum propagation speed is considered. For certain types of initial data, ‘waiting time’ phenomena are encountered.Keywords
This publication has 11 references indexed in Scilit:
- On a singular initial-boundary-value problem for a reaction-diffusion equation arising from a simple model of isothermal chemical autocatalysisProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Interaction of gas frontsQuarterly of Applied Mathematics, 1992
- The development of travelling waves in a simple isothermal chemical system with general orders of autocatalysis and decayPhilosophical Transactions A, 1991
- Propagating reaction-diffusion waves in a simple isothermal quadratic autocatalytic chemical systemJournal of Engineering Mathematics, 1989
- Mathematical BiologyPublished by Springer Nature ,1989
- Differential Equations and Mathematical BiologyPublished by Springer Nature ,1983
- Waiting‐Time Behavior in a Nonlinear Diffusion EquationStudies in Applied Mathematics, 1982
- Applications of Centre Manifold TheoryPublished by Springer Nature ,1981
- The Geometry of Biological TimePublished by Springer Nature ,1980
- THE WAVE OF ADVANCE OF ADVANTAGEOUS GENESAnnals of Eugenics, 1937