H^2-boundedness of the pullback attractor for the non-autonomous SIR equations with diffusion

Abstract

We prove some regularity results for the pullback attractor of a non- autonomous SIR model with diffusion in a bounded domain Ω of Rd where d ≥ 1. We show a regularity result for the unique solution of the prob- lem. We establish a general result about (H^2(Ω))^3-boundedness of invariant sets for the associate evolution process. Then, as a consequence, we de- duce that the pullback attractor of the non-autonomous system of SIR equations with diffusion is bounded in (H^2 (Ω))^3.