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Global existence and asymptotic behavior of global smooth solutions to the Kirchhoff equations with strong nonlinear damping

  • * Corresponding author: Chengkui Zhong

    * Corresponding author: Chengkui Zhong

Ma was supported by NSFC Grant (No.11801071), Zhang was supported by NSFC Grant (No.11601117) and Zhong was supported by NSFC Grant (No.11731005)

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  • In this paper, we consider the initial boundary problem for the Kirchhoff type wave equation. We prove that the Kirchhoff wave model is globally well-posed in the sufficiently regular space $ (H^2(\Omega)\cap H^1_0(\Omega))\times H^1_0(\Omega) $, then, we also obtain that the semigroup generated by the equation has a global attractor in the corresponding phase space, in the presence of a quite general nonlinearity of supercritical growth.

    Mathematics Subject Classification: Primary: 35B41; Secondary: 35L72, 37L30.


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