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The global attractor for the wave equation with nonlocal strong damping

  • * Corresponding author: ckzhong@nju.edu.cn

    * Corresponding author: ckzhong@nju.edu.cn

The first author is supported by NSFC(11731005)

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  • The paper is devoted to establishing the long-time behavior of solutions for the wave equation with nonlocal strong damping: $ u_{tt}-\Delta u-\|\nabla u_{t}\|^{p}\Delta u_{t}+f(u) = h(x). $ It proves the well-posedness by means of the monotone operator theory and the existence of a global attractor when the growth exponent of the nonlinearity $ f(u) $ is up to the subcritical and critical cases in natural energy space.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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