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TRAVELLING WAVE SOLUTIONS FOR DOUBLY DEGENERATE REACTION–DIFFUSION EQUATIONS

Part of:Mathematical biology in generalParabolic equations and systems

Published online by Cambridge University Press:  10 March 2011

M. B. A. MANSOUR
M. B. A. MANSOUR*
Affiliation:
Department of Mathematics, Faculty of Science at Qena, South Valley University, Qena, Egypt (email: m.mansour4@hotmail.com)
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Abstract

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This paper concerns a nonlinear doubly degenerate reaction–diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest. A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed. This travelling wave behaviour is also verified by some numerical computations for a special case.

Keywords

density-dependent diffusionnonlinear degenerate parabolic equationstravelling waves

MSC classification

Secondary:35K65: Degenerate parabolic equations92B05: General biology and biomathematics

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 1 , July 2010, pp. 101 - 109
Copyright
Copyright © Australian Mathematical Society 2011

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