J Austral Math Soc Ser B 34 pp318--332, 1993.

On a nonlinear reaction-diffusion boundary-value problem: application of a Lie-Bäcklund symmetry

Philip Broadbridge and Colin Rogers

(Received 5 April 1991; revised 24 October 1991)

Abstract

By a systematic search for Lie-Bäcklund symmetries, a class of linearisable reaction-diffusion equations is obtained that has, as a canonical form, u_t = u²u_xx + 2u². One such nonlinear equation is

q_t = ¶_x[a(b - q)^-2q_x] - ma(b - q)^-2q_x - q exp(-mx)
This represents an extension of Fokas-Yortsos-Rosen equation (q = 0) to incorporate a reaction term. It is relevant to the modelling of unsaturated flow in a soil with a volumetric extraction mechanism, such as a web of plant roots. Here, a reciprocal transformation is used to solve a nonlinear boundary-value problem for transient flow into a finite layer of a soil subject to a constant flux boundary condition to compensate for such water extraction.

Browse the article

Read the article in your browser. (Print at 75% on A4 paper).

Authors

Philip Broadbridge: Department of Mathematics, University of Wollongong, Wollongong, NSW.
Colin Rogers: Department of Mathematical Sciences, Loughborough University of Technology, U.K.

Editor JAMSB(E): editor at anziamj.austms.org.au
WWW Administrator: webmaster at anziamj.austms.org.au

Last Modified: Mon Jun 26 15:27:18 2000