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Existence of Reaction-Diffusion Waves with Nonlinear BoundaryConditions

Published online by Cambridge University Press:  12 June 2013

N. Apreutesei ,
A. Tosenberger  and
V. Volpert
N. Apreutesei
Affiliation:
Department of Mathematics, “Gheorghe Asachi" Technical University Bd. Carol. I, 700506 Iasi, Romania
A. Tosenberger
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
V. Volpert*
Affiliation:
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
*
⋆ Corresponding author. E-mail: volpert@math.univ-lyon1.fr
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Abstract

The paper is devoted to a reaction-diffusion equation in an infinite two-dimensionalstrip with nonlinear boundary conditions. The existence of travelling waves is proved inthe bistable case by the Leray-Schauder method. It is based on a topological degree forelliptic problems in unbounded domains and on a priori estimates of solutions.

Keywords

reaction-diffusion equationnonlinear boundary conditiontravelling waveLeray-Schauder method
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 3: Front Propagation , 2013 , pp. 2 - 17
Copyright
© EDP Sciences, 2013

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References

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