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The Quarterly Journal of Mechanics and Applied Mathematics 2001 54(1):157-175; doi:10.1093/qjmam/54.1.157
© 2001 by Oxford University Press
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The evolution of travelling waves in generalized Fisher equations via matched asymptotic expansions: algebraic corrections

J. A. Leach1 and D. J. Needham1

( 1 Department of Mathematics, University of Reading, Reading RG6 6AX )

In this paper we address an initial-boundary-value problem for a generalized Fisher equation. In particular, we use the method of matched asymptotic expansions to develop a rational approach for determining the propagation speed for the large-t(time) travelling wave structures which evolve in the initial-boundary-value problem. This approach resolves apparent paradoxes which arise in the much used linearized approximation (in the cases R(u) <= uand R(u) u, where R(u)is the associated reaction function) and is readily adaptable to systems of Fisher–Kolmogorov type and to problems in higher spatial dimensions.

Received 31 January, 2000. Revised 15 July, 2000.


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