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Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations

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Abstract

We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity f(u), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors in the topology of \(H_{X,0}^1(\Omega )\).

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Acknowledgements

The authors would like to thank the referees for the careful reading of this paper and for the valuable suggestions to improve the presentation and the style of the paper. This paper is supported by the Innovative Funds Plan of Henan University of Technology (No.2020ZKCJ09) and National Natural Science Foundation of China (No. 11801145 and No. 12071364).

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  1. School of Science, Henan University of Technology, Zhengzhou, 450001, China

    Gongwei Liu

  2. School of Science, Wuhan University of Technology, Wuhan, 430070, China

    Shuying Tian

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  1. Gongwei Liu
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Correspondence to Gongwei Liu.

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Liu, G., Tian, S. Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations. J. Evol. Equ. 24, 17 (2024). https://doi.org/10.1007/s00028-024-00945-y

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