GLOBAL ATTRACTOR FOR A CLASS OF REACTION-DIFFUSION SYSTEMS
DOI:
https://doi.org/10.18173/2354-1059.2026-%25xKeywords:
Reaction-diffusion system, limit system, Global attractor, upper-semicontinuityAbstract
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.
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