Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces
In this study, we primarily investigate the asymptotic behavior of solutions associated with a nonclassical diffusion process by memory effects and a perturbed parameter that varies over time. A significant innovation is the consideration of a delay term governed by a function with minimal assumptio...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024320 |
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| author | Yadan Shi Yongqin Xie Ke Li Zhipiao Tang |
| author_facet | Yadan Shi Yongqin Xie Ke Li Zhipiao Tang |
| author_sort | Yadan Shi |
| collection | DOAJ |
| description | In this study, we primarily investigate the asymptotic behavior of solutions associated with a nonclassical diffusion process by memory effects and a perturbed parameter that varies over time. A significant innovation is the consideration of a delay term governed by a function with minimal assumptions: merely measurability and a phase-space that is a time-dependent space of continuously-time-varying functions. By employing a novel analytical approach, we demonstrate the existence and regularity of time-varying pullback $ \mathscr{D} $-attractors. Notably, the nonlinearity $ f $ is unrestricted by any upper limit on its growth rate. |
| format | Article |
| id | doaj-art-4250d99dfc3747318e8bd41656e1fcfa |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-4250d99dfc3747318e8bd41656e1fcfa2025-01-23T07:53:07ZengAIMS PressElectronic Research Archive2688-15942024-12-0132126847686810.3934/era.2024320Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spacesYadan Shi0Yongqin Xie1Ke Li2Zhipiao Tang3School of General Education, Hunan University of Information Technology, Changsha 410151, ChinaSchool of General Education, Hunan University of Information Technology, Changsha 410151, ChinaSchool of General Education, Hunan University of Information Technology, Changsha 410151, ChinaSchool of General Education, Hunan University of Information Technology, Changsha 410151, ChinaIn this study, we primarily investigate the asymptotic behavior of solutions associated with a nonclassical diffusion process by memory effects and a perturbed parameter that varies over time. A significant innovation is the consideration of a delay term governed by a function with minimal assumptions: merely measurability and a phase-space that is a time-dependent space of continuously-time-varying functions. By employing a novel analytical approach, we demonstrate the existence and regularity of time-varying pullback $ \mathscr{D} $-attractors. Notably, the nonlinearity $ f $ is unrestricted by any upper limit on its growth rate.https://www.aimspress.com/article/doi/10.3934/era.2024320nonclassical diffusion equationpullback attractorsnonlinear delaypolynomial growth |
| spellingShingle | Yadan Shi Yongqin Xie Ke Li Zhipiao Tang Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces Electronic Research Archive nonclassical diffusion equation pullback attractors nonlinear delay polynomial growth |
| title | Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces |
| title_full | Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces |
| title_fullStr | Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces |
| title_full_unstemmed | Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces |
| title_short | Attractors for the nonclassical diffusion equations with the driving delay term in time-dependent spaces |
| title_sort | attractors for the nonclassical diffusion equations with the driving delay term in time dependent spaces |
| topic | nonclassical diffusion equation pullback attractors nonlinear delay polynomial growth |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024320 |
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