Pullback attractors for the nonclassical diffusion equations with memory in time-dependent spaces

Ke Li; Yongqin Xie; Yong Ren; Jun Li; Ke Li; Yongqin Xie; Yong Ren; Jun Li

doi:10.3934/math.20231561

AIMS Mathematics

2023, Volume 8, Issue 12: 30537-30561. doi: 10.3934/math.20231561

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Pullback attractors for the nonclassical diffusion equations with memory in time-dependent spaces

1.
School of General Education, Hunan University of Information Technology, Changsha, Hunan 410151, China
2.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China

Received: 01 September 2023 Revised: 27 October 2023 Accepted: 05 November 2023 Published: 10 November 2023
MSC : 35K57, 35B40, 35B41, 45K05

In this paper, we consider the asymptotic behavior of nonclassical diffusion equations with hereditary memory and time-dependent perturbed parameter on whole space $ \mathbb{R}^n $. Under a general assumption on the memory kernel $ k $, the existence and regularity of time-dependent global attractors are proven using a new analytical technique. It is remarkable that the nonlinearity $ f $ has no restriction on the upper growth.
- nonclassical diffusion equation,
- time-dependent global attractor,
- memory,
- unbounded domain
Citation: Ke Li, Yongqin Xie, Yong Ren, Jun Li. Pullback attractors for the nonclassical diffusion equations with memory in time-dependent spaces[J]. AIMS Mathematics, 2023, 8(12): 30537-30561. doi: 10.3934/math.20231561

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Abstract

In this paper, we consider the asymptotic behavior of nonclassical diffusion equations with hereditary memory and time-dependent perturbed parameter on whole space $ \mathbb{R}^n $. Under a general assumption on the memory kernel $ k $, the existence and regularity of time-dependent global attractors are proven using a new analytical technique. It is remarkable that the nonlinearity $ f $ has no restriction on the upper growth.

References

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