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

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.