GLOBAL ATTRACTOR FOR A CLASS OF REACTION-DIFFUSION SYSTEMS

DOI: 10.18173/2354-1059.2026-0002

Abstract

We study the initial boundary value problem for a class of reaction-diffusion systems in bounded smooth domains, where one equation has a small diffusion coefficient δ > 0, and also the corresponding limit system is formally obtained when δ = 0. We prove the existence of global attractor Aδ for the dynamical system generated by the system in both cases δ > 0 and δ = 0. Moreover, the upper semicontinuity of the global attractor Aδ at δ = 0 is also investigated.