Existence and regularity of time-dependent pullback attractors for the non-autonomous nonclassical diffusion equations. Issue 6 (December 2022)

• Record Type: Journal Article
• Authors: Qin, Yuming; Yang, Bin
• Is Part Of: Proceedings. Volume 152:Issue 6(2022)
• Page Start: 1533
• Page End: 1550
• Publication Date: 2022-12
• Subjects: Non-autonomous nonclassical diffusion equations -- time-dependent pullback attractors -- regularity; 35B40 -- 35B41 -- 35B65 -- 35K57; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2021.65
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : In this paper, we prove the existence and regularity of pullback attractors for non-autonomous nonclassical diffusion equations with nonlocal diffusion when the nonlinear term satisfies critical exponential growth and the external force term $h \in L_{l o c}^{2}(\mathbb {R} ; H^{-1}(\Omega )).$ Under some appropriate assumptions, we establish the existence and uniqueness of the weak solution in the time-dependent space $\mathcal {H}_{t}(\Omega )$ and the existence and regularity of the pullback attractors.