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Annihilation dynamics in the KPP-Fisher equation

Published online by Cambridge University Press:  16 April 2002

M. RODRIGO
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology, 606 Cullimore Hall, University Heights, Newark, NJ 07102, USA e-mail: mrodrigo@math.sci.hiroshima-u.ac.jp
M. MIMURA
Affiliation:
Institute for Nonlinear Sciences and Applied Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan e-mail: mimura@math.sci.hiroshima-u.ac.jp

Abstract

We study the annihilation dynamics arising in the KPP-Fisher equation, proposed by Fisher in 1936 to model the propagation of a mutant gene and subsequently studied rigorously in the seminal work of Kolmogorov, Petrovskii and Piskunov. The approach is via a comparison theorem, where the comparison functions satisfy equations which are linearizable to the heat equation. In some sense, we have obtained a ‘linearization’ of the KPP-Fisher equation.

Type
Research Article
Copyright
2002 Cambridge University Press

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