Time-dependent asymptotic behavior of the solution for evolution equation with linear memory
In this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent at...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023829?viewType=HTML |
| _version_ | 1797822568267251712 |
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| author | Tingting Liu Tasneem Mustafa Hussain Sharfi Qiaozhen Ma |
| author_facet | Tingting Liu Tasneem Mustafa Hussain Sharfi Qiaozhen Ma |
| author_sort | Tingting Liu |
| collection | DOAJ |
| description | In this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent attractor are proved, which means that the time-dependent attractor of the evolution equation converges to the attractor of the limit wave equation when the coefficient $ \varepsilon(t)\rightarrow0 $ as $ t\rightarrow \infty $. |
| first_indexed | 2024-03-13T10:11:02Z |
| format | Article |
| id | doaj.art-e894784de754448ea940145e8814732f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T10:11:02Z |
| publishDate | 2023-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e894784de754448ea940145e8814732f2023-05-22T01:17:19ZengAIMS PressAIMS Mathematics2473-69882023-05-0187162081622710.3934/math.2023829Time-dependent asymptotic behavior of the solution for evolution equation with linear memoryTingting Liu0Tasneem Mustafa Hussain Sharfi 1Qiaozhen Ma21. College of Mathematics and Statistics, Northwest Normal University, Gansu, 730070, Lanzhou, China2. Faculty of Mathematical science, University of Khartoum, Sudan1. College of Mathematics and Statistics, Northwest Normal University, Gansu, 730070, Lanzhou, ChinaIn this article, by using the operator decomposition technique, we discuss the existence of a time-dependent global attractor for a nonlinear evolution equation with linear memory within the theory of time-dependent space. Furthermore, the regularity and asymptotic structure of the time-dependent attractor are proved, which means that the time-dependent attractor of the evolution equation converges to the attractor of the limit wave equation when the coefficient $ \varepsilon(t)\rightarrow0 $ as $ t\rightarrow \infty $. https://www.aimspress.com/article/doi/10.3934/math.2023829?viewType=HTMLlinear memorytime-dependent global attractorregularityasymptotic structure |
| spellingShingle | Tingting Liu Tasneem Mustafa Hussain Sharfi Qiaozhen Ma Time-dependent asymptotic behavior of the solution for evolution equation with linear memory AIMS Mathematics linear memory time-dependent global attractor regularity asymptotic structure |
| title | Time-dependent asymptotic behavior of the solution for evolution equation with linear memory |
| title_full | Time-dependent asymptotic behavior of the solution for evolution equation with linear memory |
| title_fullStr | Time-dependent asymptotic behavior of the solution for evolution equation with linear memory |
| title_full_unstemmed | Time-dependent asymptotic behavior of the solution for evolution equation with linear memory |
| title_short | Time-dependent asymptotic behavior of the solution for evolution equation with linear memory |
| title_sort | time dependent asymptotic behavior of the solution for evolution equation with linear memory |
| topic | linear memory time-dependent global attractor regularity asymptotic structure |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023829?viewType=HTML |
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