Stability of reaction fronts in thin domains

The paper is devoted to the stability of reaction fronts in thin domains. The influence of natural convection and of heat losses through the walls of the reactor is studied numerically and analytically. Critical conditions of stability of stationary solutions are obtained. 1. Introduction. The stability of reaction fronts is important for many technological devices and it is interesting from the point of view of nonlinear dynamics (see [6] and the references therein). It is known that thermal instability can be strongly influenced by heat loss [1] especially near the extinction limit. In this work, we study the influence of heat loss and of convection on thermal fronts in thin domains, where we can reduce the space dimension of the problem and in some cases simplify its analysis. We consider the system of equations where the reaction-diffusion system is coupled with the Navier-Stokes equations under the Boussinesq approximation to describe natural convection which can occur because of the heat produced by the reaction: