Existence of radial stationary solutions for a system in combustion theory

Jérôme Coville (1) , Juan Davila (2)

1 BioSP - Biostatistique et Processus Spatiaux
2 DIM - Departamento de Ingenieria Matemàtica and CMM

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative 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.

Mots clés: Elliptic system; radial solutions; combustion model; flame balls; flame balls.

Domaines: Equations aux dérivées partielles [math.AP]

Jérôme Coville, Juan Davila. Existence of radial stationary solutions for a system in combustion theory. Discrete and Continuous Dynamical Systems - Series B, 2011, 16 (3), ⟨10.3934/dcdsb.2011.16.xx⟩. ⟨hal-00603865⟩