The Mathematical Institute, University of Oxford, Eprints Archive

A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations

Sánchez-Garduño, F. and Kappos, E. and Maini, P. K. (1996) A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations. IMA Journal of Applied Mathematics, 57 (3). pp. 211-221.

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Abstract

In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c*>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation.

Item Type:Article
Uncontrolled Keywords:n/a
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:462
Deposited By:Philip Maini
Deposited On:06 Dec 2006
Last Modified:20 Jul 2009 14:21

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