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

Published online by Cambridge University Press:  17 February 2009

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

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By a systematic search for Lie-Bäetcklund symmetries, a class of linearisable reaction-diffusion equations is obtained that has, as a canonical form, ut = u2uxx + 2u2. One such nonlinear equation is θt = ∂x[a(b - θ)-2 θx] - ma(b -θ)-2 θx - 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 318 - 332
Copyright
Copyright © Australian Mathematical Society 1993

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