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

Article type: Research Article

Authors: Glangetas, L.

Affiliations: Laboratoire d'analyse numérique, tour 55–65, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France

Abstract: We consider solutions (uε,vε,cε) of a system of two nonlinear differential equations −u″ε+cεu′ε=fε(uε)vε, −Λv″ε+cεv′ε=−fε(uε)vε on R with the boundary conditions uε(−∞)=0, uε(+∞)=1, vε(−∞)=1, vε(+∞)=0. We investigate the asymptotic behavior of (uε,vε,cε) as ε→0 and fε(u)(1−u) behaves as a Dirac distribution. This singular limit corresponds to some combustion models (planar flame propagations) for high activation energy asymptotics.

DOI: 10.3233/ASY-1992-5403

Journal: Asymptotic Analysis, vol. 5, no. 4, pp. 317-342, 1992