An upper bound for the temperature for some combustion equations in the limit of large activation energy

Article type: Research Article

Authors: Langlois, A. | Marion, M.^;

Affiliations: UMR CNRS 5585, Ecole Centrale de Lyon, Département Mathématiques et Informatique, BP 163, 69131 Ecully Cedex, France

Note: [] Corresponding author.

Abstract: This paper is concerned with the thermal diffusional model borrowed from the theory of combustion. The analytic methods currently used to investigate this model require a near‐equidiffusion condition, the inverse of the activation energy being the small parameter. The first step in these methods consists in assuming a suitable bound on the temperature. The aim of this paper is to derive rigorously such a bound. We show that the temperature is bounded independently of the activation energy β uniformly in time, at least for sufficiently large values of β. The proof relies on the use of a Lyapunov function first introduced by Barabanova [1] and energy type estimates.

Keywords: Reaction‐diffusion systems, combustion, uniform estimates

Journal: Asymptotic Analysis, vol. 23, no. 3-4, pp. 195-216, 2000