Dynamic of the nonclassical diffusion equation with memory
Abstract In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space. First, the well-posedness of the solution for the equation is obtained in the time-dependent space U t $\mathscr...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-08-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01767-6 |
| _version_ | 1797451942349242368 |
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| author | Jing Wang Qiaozhen Ma Wenxue Zhou Xiaobin Yao |
| author_facet | Jing Wang Qiaozhen Ma Wenxue Zhou Xiaobin Yao |
| author_sort | Jing Wang |
| collection | DOAJ |
| description | Abstract In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space. First, the well-posedness of the solution for the equation is obtained in the time-dependent space U t $\mathscr{U}_{t}$ . Then, we establish the existence and regularity of the time-dependent global attractor. Finally, we also conclude that the fractal dimension of the time-dependent attractor is finite. |
| first_indexed | 2024-03-09T15:01:45Z |
| format | Article |
| id | doaj.art-23e664c45c7448b9944fe9f5e061484a |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-09T15:01:45Z |
| publishDate | 2023-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-23e664c45c7448b9944fe9f5e061484a2023-11-26T13:51:09ZengSpringerOpenBoundary Value Problems1687-27702023-08-012023112210.1186/s13661-023-01767-6Dynamic of the nonclassical diffusion equation with memoryJing Wang0Qiaozhen Ma1Wenxue Zhou2Xiaobin Yao3School of Mathematics and Physics, Lanzhou Jiaotong UniversityCollege of Mathematics and Statistics, Northwest Normal UniversitySchool of Mathematics and Physics, Lanzhou Jiaotong UniversityCollege of Mathematics and Statistics, Qinghai Minzu UniversityAbstract In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space. First, the well-posedness of the solution for the equation is obtained in the time-dependent space U t $\mathscr{U}_{t}$ . Then, we establish the existence and regularity of the time-dependent global attractor. Finally, we also conclude that the fractal dimension of the time-dependent attractor is finite.https://doi.org/10.1186/s13661-023-01767-6Nonclassical diffusion equationTime-dependent global attractorPolynomial growth of arbitrary orderRegularityFinite fractal dimension |
| spellingShingle | Jing Wang Qiaozhen Ma Wenxue Zhou Xiaobin Yao Dynamic of the nonclassical diffusion equation with memory Boundary Value Problems Nonclassical diffusion equation Time-dependent global attractor Polynomial growth of arbitrary order Regularity Finite fractal dimension |
| title | Dynamic of the nonclassical diffusion equation with memory |
| title_full | Dynamic of the nonclassical diffusion equation with memory |
| title_fullStr | Dynamic of the nonclassical diffusion equation with memory |
| title_full_unstemmed | Dynamic of the nonclassical diffusion equation with memory |
| title_short | Dynamic of the nonclassical diffusion equation with memory |
| title_sort | dynamic of the nonclassical diffusion equation with memory |
| topic | Nonclassical diffusion equation Time-dependent global attractor Polynomial growth of arbitrary order Regularity Finite fractal dimension |
| url | https://doi.org/10.1186/s13661-023-01767-6 |
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