Existence of radial stationary solutions for a system in combustion theory

Jérôme Coville; Juan Dávila

doi:10.3934/dcdsb.2011.16.739

Article Contents

2011, Volume 16, Issue 3: 739-766. Doi: 10.3934/dcdsb.2011.16.739

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Existence of radial stationary solutions for a system in combustion theory

Jérôme Coville^1, and
Juan Dávila^2,

1.
INRA, Equipe BIOSP, Centre de Recherche d'Avignon, Domaine Saint Paul, Site Agroparc, 84914 Avignon cedex 9
2.
Departamento de Ingeniería Matemática and CMM (UMI 2807 CNRS), Universidad de Chile, Blanco Encalada 2120 - 5 Piso, Santiago

Received: May 31, 2010

Revised: January 31, 2011

Published: September 2011

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Abstract

In this paper, we construct radially symmetric solutions of a nonlinear non-cooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory.

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Mathematics Subject Classification: Primary: 35J60, 35J47; Secondary: 80A25.

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