Etude d'une limite singulière d'un modèle intervenant en combustion

Abstract

We consider solutions (u_ε,v_ε,c_ε) of a system of two nonlinear differential equations −u″_ε+c_εu′_ε=f_ε(u_ε)v_ε, −Λv″_ε+c_εv′_ε=−f_ε(u_ε)v_ε on R with the boundary conditions u_ε(−∞)=0, u_ε(+∞)=1, v_ε(−∞)=1, v_ε(+∞)=0. We investigate the asymptotic behavior of (u_ε,v_ε,c_ε) as ε→0 and f_ε(u)(1−u) behaves as a Dirac distribution. This singular limit corresponds to some combustion models (planar flame propagations) for high activation energy asymptotics.