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Bi-spatial Pullback Attractors of Non-autonomous p-Laplacian Equations on Unbounded Thin Domains

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Abstract

In this paper we study the bi-spatial dynamics of non-autonomous parabolic equations with nonlinear Laplacian on \(n+1\)-dimensional unbounded thin domains, where the nonlinearity has a (p, q)-growth exponents. We first prove the existence and uniqueness of tempered pullback attractors in \( L^2\) on \(n+1\)-dimensional unbounded thin domains, and then obtain the upper semi-continuity of these attractors in \(L^2\) when the \(n+1\)-dimensional thin domains degenerates onto a n-dimensional entire space \({\mathbb {R}}^n\). Finally by borrowing an inductive method and a bootstrap technique, we show that the difference of solutions near the initial time is higher-order integrable for any space dimension \(n\ge 1\), which further shows the existence of pullback attractors in \( L^p\cap L^q\). Based on the higher-order integrability, we find that the obtained pullback attractor is attracting under the topology of \(L^\delta \) with \(\delta \in [2,\infty )\).

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Funding

Fuzhi Li was supported by the NSFC (12201415) and the Jiangxi Provincial Natural Science Foundation (20224BAB201009, 20202BABL211006). M. M. Freitas thank the CNPq for financial support through the project Attractors and asymptotic behavior of nonlinear evolution equations by Grant 313081/2021-2. Jiali Yu was supported by the Natural Science Research Project of the Educational Department of Liaoning Province (JDL2020027).

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Authors and Affiliations

  1. School of Mathematics & Computer Science, Shangrao Normal University, Shangrao, 334001, China

    Fuzhi Li

  2. Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street, Salinópolis, PA, 68721-000, Brazil

    Mirelson M. Freitas

  3. School of Science, Dalian Jiaotong University, Dalian, 116028, China

    Jiali Yu

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  1. Fuzhi Li
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  2. Mirelson M. Freitas
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  3. Jiali Yu
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Each of the authors contributed to each part of this study equally. All authors read and proved the final vision of the manuscript.

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Correspondence to Mirelson M. Freitas.

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Li, F., Freitas, M.M. & Yu, J. Bi-spatial Pullback Attractors of Non-autonomous p-Laplacian Equations on Unbounded Thin Domains. Appl Math Optim 88, 18 (2023). https://doi.org/10.1007/s00245-023-10001-9

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