The Mathematical Institute, University of Oxford, Eprints Archive

A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term

Sánchez-Garduño, F. and Maini, P. K. and Kappos, E. (1996) A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term. FORMA, 11 (1). pp. 45-59.

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Abstract

In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:569
Deposited By:Philip Maini
Deposited On:19 Feb 2007
Last Modified:20 Jul 2009 14:22

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