Reaction-diffusion waves with nonlinear boundary conditions

Narcisa Apreutesei; Vitaly Volpert; Narcisa Apreutesei; Vitaly Volpert

doi:10.3934/nhm.2013.8.23

Networks and Heterogeneous Media

2013, Volume 8, Issue 1: 23-35. doi: 10.3934/nhm.2013.8.23

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Reaction-diffusion waves with nonlinear boundary conditions

Narcisa Apreutesei ^{1
,},
Vitaly Volpert ^{2
,}

1.
Department of Mathematics, "Gheorghe Asachi" Technical University, Bd. Carol. I, 700506 Iasi
2.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne

Received: 01 January 2012 Revised: 01 July 2012
Primary: 35K57; Secondary: 35J60.

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method.
- Travelling waves,
- nonlinear boundary conditions,
- existence,
- Leray-Schauder method
Citation: Narcisa Apreutesei, Vitaly Volpert. Reaction-diffusion waves with nonlinear boundary conditions[J]. Networks and Heterogeneous Media, 2013, 8(1): 23-35. doi: 10.3934/nhm.2013.8.23

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Abstract

A reaction-diffusion equation with nonlinear boundary condition is considered in a two-dimensional infinite strip. Existence of waves in the bistable case is proved by the Leray-Schauder method.

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