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Singular limits for travelling waves for a pair of equations*

Published online by Cambridge University Press:  14 November 2011

Vivian Hutson  and
Konstantin Mischaikow
Vivian Hutson
Affiliation:
Department of Applied Mathematics, The University of Sheffield, Sheffield S3 7RH, U.K.
Konstantin Mischaikow
Affiliation:
Cenlcr for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.mischaik@math.gatech.edu
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Extract

The singular limit as one diffusion coefficient approaches zero is considered for travelling wave solutions to a pair f reaction diffusion equations. An explicit criterion determining the sign of the wave speed is obtained. The limit behaviour turns out to be of a different nature for positive and negative wave speed. Different techniques, which may be applicable to a range of examples, are needed in the two cases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 2 , 1996 , pp. 399 - 411
Copyright
Copyright © Royal Society of Edinburgh 1996

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