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

Yan Zhang and Jin Zhang ()
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Yan Zhang: School of Mathematics, Hohai University, Nanjing 210098, China
Jin Zhang: School of Mathematics, Hohai University, Nanjing 210098, China

Mathematics, 2024, vol. 12, issue 21, 1-10

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 L 2 ( Ω ) × L μ 2 ( R ; H 0 1 ( 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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