Existence of a Global Attractor for the Reaction–Diffusion Equation with Memory and Lower Regularity Terms

Abstract

This paper investigates the large time behavior for the reaction–diffusion equation with memory and the forcing term g∈H−1(Ω). We prove the existence of a global attractor in L2(Ω)×Lμ2(R;H01(Ω)). Due to the lower regularity of g, one can hardly use the traditional energy estimates to derive the existence of a bounded absorbing set in the higher regularity space and then the compactness of the semigroup. Here, we utilize the contractive function method to establish the asymptotic smoothness of the semigroup.

Keywords

• global attractor
• reaction–diffusion equation
• memory term
• lower regularity
• asymptotically smooth