IJPAM: Volume 27, No. 2 (2006)


A. Ducrot$^1$, M. Marion$^2$, V. Volpert$^3$
$^{1,2}$Laboratoire de Mathématiques Appliquées
UMR 5585 CNRS, Ecole Centrale de Lyon
Ecully, 69134, FRANCE
$^3$Laboratoire de Mathématiques Appliquées
UMR 5585 CNRS, Université Lyon 1
Villeurbanne, 69622, FRANCE

Abstract.The paper is devoted to a reaction-diffusion-convection problem posed in an infinite strip. Problems of this type describe flame propagation with natural convection. If the Lewis number is different from $1$, then the corresponding elliptic operator does not satisfy the Fredholm property, and the conventional methods of nonlinear analysis are not applicable. We reduce the system to an integro-differential system of equations and prove the existence of reaction-diffusion-convection waves for Lewis number close to $1$.

Received: September 9, 2005

AMS Subject Classification: 47A53, 76D05, 35Q30

Key Words and Phrases: reaction-diffusion-convection problems, Fredholm operators, Lewis number, integro-differential system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 27
Issue: 2