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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024320 |
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| Summary: | 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. |
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| ISSN: | 2688-1594 |