Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces
Abstract In this paper, based on the notation of time-dependent attractors introduced by Conti, Pata and Temam in (J. Differ. Equ. 255:1254–1277, 2013), we prove the existence of time-dependent global attractors in H t $\mathcal{H}_{t}$ for a class of nonclassical reaction–diffusion equations with t...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01392-7 |
| _version_ | 1819228569129189376 |
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| author | Kaixuan Zhu Yongqin Xie Feng Zhou |
| author_facet | Kaixuan Zhu Yongqin Xie Feng Zhou |
| author_sort | Kaixuan Zhu |
| collection | DOAJ |
| description | Abstract In this paper, based on the notation of time-dependent attractors introduced by Conti, Pata and Temam in (J. Differ. Equ. 255:1254–1277, 2013), we prove the existence of time-dependent global attractors in H t $\mathcal{H}_{t}$ for a class of nonclassical reaction–diffusion equations with the forcing term g ( x ) ∈ H − 1 ( Ω ) $g(x)\in H^{-1}(\varOmega )$ and the nonlinearity f satisfying the polynomial growth of arbitrary p − 1 $p-1$ ( p ≥ 2 $p\geq 2$ ) order, which generalizes the results obtained in (Appl. Anal. 94:1439–1449, 2015) and (Bound. Value Probl. 2016: 10, 2016). |
| first_indexed | 2024-12-23T10:59:22Z |
| format | Article |
| id | doaj.art-051daf87c247490fa908e53785186b9e |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-23T10:59:22Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-051daf87c247490fa908e53785186b9e2022-12-21T17:49:40ZengSpringerOpenBoundary Value Problems1687-27702020-05-012020111410.1186/s13661-020-01392-7Attractors for the nonclassical reaction–diffusion equations on time-dependent spacesKaixuan Zhu0Yongqin Xie1Feng Zhou2Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, College of Mathematics and Physics Science, Hunan University of Arts and ScienceSchool of Mathematics and Statistics, Changsha University of Science and TechnologyCollege of Science, China University of Petroleum (East China)Abstract In this paper, based on the notation of time-dependent attractors introduced by Conti, Pata and Temam in (J. Differ. Equ. 255:1254–1277, 2013), we prove the existence of time-dependent global attractors in H t $\mathcal{H}_{t}$ for a class of nonclassical reaction–diffusion equations with the forcing term g ( x ) ∈ H − 1 ( Ω ) $g(x)\in H^{-1}(\varOmega )$ and the nonlinearity f satisfying the polynomial growth of arbitrary p − 1 $p-1$ ( p ≥ 2 $p\geq 2$ ) order, which generalizes the results obtained in (Appl. Anal. 94:1439–1449, 2015) and (Bound. Value Probl. 2016: 10, 2016).http://link.springer.com/article/10.1186/s13661-020-01392-7Nonclassical reaction–diffusion equationsPolynomial growth of arbitrary orderTime-dependent global attractors |
| spellingShingle | Kaixuan Zhu Yongqin Xie Feng Zhou Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces Boundary Value Problems Nonclassical reaction–diffusion equations Polynomial growth of arbitrary order Time-dependent global attractors |
| title | Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces |
| title_full | Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces |
| title_fullStr | Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces |
| title_full_unstemmed | Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces |
| title_short | Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces |
| title_sort | attractors for the nonclassical reaction diffusion equations on time dependent spaces |
| topic | Nonclassical reaction–diffusion equations Polynomial growth of arbitrary order Time-dependent global attractors |
| url | http://link.springer.com/article/10.1186/s13661-020-01392-7 |
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