In this paper, we consider the long-time behavior of the nonclassical diffusion equation with perturbed parameter and memory on a bounded domain . The main feature of this model is that the equation contains a dissipative term with perturbation parameters −νΔu and the nonlinearity f satisfies the polynomial growth of arbitrary order. By using the nonclassical operator method and a new analytical method (or technique) (Lemma 2.7), the existence and regularity of uniform attractors generated for this equation are proved. Furthermore, we also get the upper semicontinuity of the uniform attractors when the perturbed parameter ν → 0. It is remarkable that if ν = 0, we can get the same conclusion as in the works of Toan et al. [Acta Appl. Math. 170, 789–822 (2020)] and Conti et al. [Commun. Pure Appl. Anal. 19, 2035–2050 (2020)], but the nonlinearity is critical.
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February 2023
Research Article|
February 03 2023
Uniform attractors for nonclassical diffusion equations with perturbed parameter and memory
Yongqin Xie;
Yongqin Xie
(Funding acquisition, Methodology, Supervision, Validation, Writing – original draft)
1
School of Mathematics and Statistics, Changsha University of Science and Technology
, Changsha 410114, People’s Republic of China
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Di Liu
;
Di Liu
a)
(Visualization, Writing – original draft)
1
School of Mathematics and Statistics, Changsha University of Science and Technology
, Changsha 410114, People’s Republic of China
a)Author to whom correspondence should be addressed: liudmath@163.com
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Jiangwei Zhang
;
Jiangwei Zhang
(Visualization, Writing – original draft, Writing – review & editing)
2
College of Science, National University of Defense Technology
, Changsha 410073, People’s Republic of China
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Ximeng Liu
Ximeng Liu
a)
(Visualization)
1
School of Mathematics and Statistics, Changsha University of Science and Technology
, Changsha 410114, People’s Republic of China
a)Author to whom correspondence should be addressed: liudmath@163.com
Search for other works by this author on:
a)Author to whom correspondence should be addressed: liudmath@163.com
J. Math. Phys. 64, 022701 (2023)
Article history
Received:
August 22 2021
Accepted:
January 09 2023
Citation
Yongqin Xie, Di Liu, Jiangwei Zhang, Ximeng Liu; Uniform attractors for nonclassical diffusion equations with perturbed parameter and memory. J. Math. Phys. 1 February 2023; 64 (2): 022701. https://doi.org/10.1063/5.0068029
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