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Long-Time Dynamics of Stochastic Lattice Plate Equations with Nonlinear Noise and Damping

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Abstract

In this article we investigate the global existence as well as long-term dynamics for a wide class of lattice plate equations on the entire integer set with nonlinear damping driven by infinite-dimensional nonlinear noise. The well-posedness of the system is established for a class of nonlinear drift functions of polynomial growth of arbitrary order as well as locally Lipschitz continuous diffusion functions depending on time. Both existence and uniqueness of weak pullback mean random attractors are established for the non-autonomous system when the growth rate of the drift function is almost linear. In addition, the existence of invariant measures for the autonomous system is also established in \(\ell ^2\times \ell ^2\) when the growth rate of the drift function is superlinear. The main difficulty of deriving the tightness of a family of distribution laws of the solutions is surmounted in light of the idea of uniform tail-estimates on the solutions developed by Wang (Phys D 128:41–52, 1999).

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Acknowledgements

The author was supported by the China Scholarship Council (CSC No. 201806990064). This work was done when the author visited the Department of Mathematics at the New Mexico Institute of Mining and Technology. He would like to express his thanks to all people there for their kind hospitality.

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  1. Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing, 100088, China

    Renhai Wang

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  1. Renhai Wang
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Correspondence to Renhai Wang.

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Wang, R. Long-Time Dynamics of Stochastic Lattice Plate Equations with Nonlinear Noise and Damping. J Dyn Diff Equat 33, 767–803 (2021). https://doi.org/10.1007/s10884-020-09830-x

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