Asymptotic Regularity and Existence of Time-Dependent Attractors for Second-Order Undamped Evolution Equations with Memory

Xuan Wang, Didi Hu and Chenghua Gao
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Xuan Wang: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Didi Hu: State Key Laboratory of Cryospheric Science, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730070, China
Chenghua Gao: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2022, vol. 10, issue 13, 1-21

Abstract: Our purpose in this article is to study the asymptotic behavior of undamped evolution equations with fading memory on time-dependent spaces. By means of the theory of processes on time-dependent spaces, asymptotic a priori estimate and the technique of operator decomposition and the existence and asymptotic regularity of time-dependent attractors are, respectively, established in the critical case. At the same time, we also obtain the asymptotic regularity of the solution.

Keywords: asymptotic regularity; time-dependent attractor; undamped evolution equation; fading memory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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