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Uniform attractors for non-autonomous plate equations with $ p $-Laplacian perturbation and critical nonlinearities

  • * Corresponding author: Marcelo J. D. Nascimento

    * Corresponding author: Marcelo J. D. Nascimento 

The first author is partially supported by the Key Project of Science and Technology of Henan Province (Grant No. 182102410069) and the Fund of Young Backbone Teacher in Henan Province (No. 2018GGJS039)
The second author is partially supported by FAPESP grant # 2017/06582-2, Brazil

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  • This paper is concerned with the long-time behavior for a class of non-autonomous plate equations with perturbation and strong damping of $ p $-Laplacian type

    $ u_{tt} + \Delta^2 u + a_{\epsilon}(t) u_t - \Delta_p u - \Delta u_t + f(u) = g(x,t), $

    in bounded domain $ \Omega\subset \mathbb{R}^N $ with smooth boundary and critical nonlinear terms. The global existence of weak solution which generates a continuous process has been presented firstly, then the existence of strong and weak uniform attractors with non-compact external forces also derived. Moreover, the upper-semicontinuity of uniform attractors under small perturbations has also obtained by delicate estimate and contradiction argument.

    Mathematics Subject Classification: Primary: 35L75, 37B55; Secondary: 35B41, 74K20.


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