The Mathematical Institute, University of Oxford, Eprints Archive

An approximation to a sharp type solution of a density-dependent diffusion equation

Sánchez-Garduño, F. and Maini, P. K. (1994) An approximation to a sharp type solution of a density-dependent diffusion equation. Applied Mathematics Letters, 7 (1). pp. 47-51.

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Abstract

In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $ u(x,t) = \phi (x - ct)$. We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively.

Item Type:Article
Uncontrolled Keywords:Travelling waves; Wavespeed; Perturbation method; Sharp solutions; Density-dependent diffusion
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:495
Deposited By:Philip Maini
Deposited On:12 Dec 2006
Last Modified:20 Jul 2009 14:21

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