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

Honglv Ma; Jin Zhang; Chengkui Zhong

doi:10.3934/dcdsb.2019027

Article Contents

2019, Volume 24, Issue 9: 4721-4737. Doi: 10.3934/dcdsb.2019027

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

1.
School of Mathematics, Southeast University, Nanjing, 211189, China
2.
Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, China
3.
Department of Mathematics, Nanjing University, Nanjing, 210093, China

^* Corresponding author: Chengkui Zhong
^* Corresponding author: Chengkui Zhong

Received: July 31, 2017

Early access: February 2019

Published: July 2019

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.

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

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