Pullback Attractors for Nonclassical Diffusion Equations With a Delay Operator
ABSTRACT In this paper, we consider the asymptotic behavior of weak solutions for nonclassical nonautonomous diffusion equations with a delay operator in time‐dependent spaces when the nonlinear function satisfies subcritical exponent growth conditions, the delay operator contains some hereditary characteristics, and the external force . First, we prove the well‐posedness of solutions by using the Faedo–Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time‐dependent spaces and , respectively.
Authors
- Alain Miranville (ORCID: https://orcid.org/0000-0002-6030-5928)
- Yuming Qin (ORCID: https://orcid.org/0000-0002-1850-2362)
- Ke Wang (ORCID: https://orcid.org/0000-0001-5788-1396)
- Yang Bin (ORCID: https://orcid.org/0009-0008-4497-2334)
Institutions
- Université Le Havre Normandie (FR)
- Donghua University (CN)
- Inner Mongolia University of Science and Technology (CN)
- Laboratoire de Mathématiques Appliquées du Havre (FR)
Publication Details
- Journal
- Studies in Applied Mathematics
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1111/sapm.70039
- Citations
- 3
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 3.64
Funders
- National Natural Science Foundation of China
- Fundamental Research Funds for the Central Universities