Work

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

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12213374

Authors: Yan Zhang, Jin Zhang

Institution: Hohai University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: National Natural Science Foundation of China, China Scholarship Council