Attractors for a Bénard type problem with constraints

Abstract

In this paper, we deal with the dynamic of a model for the mass and heat transfer by a gaseous phase with an instantaneous chemical reaction, which is modeled by means of a subdifferential. To solve this problem, we use a penalization method and we prove that a maximal attractor describes the long‐time behaviour of the weak solutions. Furthermore, we prove the upper semicontinuity in $L^{2}$ of the family of attractors related to the penalization approach of this problem.