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Wave pinning in strips

Published online by Cambridge University Press:  12 July 2007

Karsten Matthies  and
C. E. Wayne
Karsten Matthies
Affiliation:
Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2–6, 14195 Berlin, Germany
C. E. Wayne
Affiliation:
Department of Mathematics and Statistics and Center for Biodynamics, Boston University, 111 Cummington Street, Boston, MA 02215, USA (cew@math.bu.edu)
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Abstract

We consider the existence of stationary or pinned waves of reaction–diffusion equations in heterogeneous media. By combining averaging, homogenization and dynamical-systems techniques we prove under mild non-degeneracy conditions that if the heterogeneity is periodic with period ε, pinned solutions persist at most for intervals in parameter space whose length is O(e−c/√ε).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 5 , October 2006 , pp. 971 - 995
Copyright
Copyright © Royal Society of Edinburgh 2006

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