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.