Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

Stéphane Gerbi; Belkacem Said-Houari

doi:10.1016/j.na.2011.07.026

Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

Stéphane Gerbi, Belkacem Said-Houari

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

Original language	English (US)
Pages (from-to)	7137-7150
Number of pages	14
Journal	Nonlinear Analysis: Theory, Methods & Applications
Volume	74
Issue number	18
DOIs	https://doi.org/10.1016/j.na.2011.07.026
State	Published - Dec 2011

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KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2011.07.026

Cite this

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abstract = "In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. {\textcopyright} 2011 Elsevier Ltd. All rights reserved.",

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AU - Said-Houari, Belkacem

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PY - 2011/12

Y1 - 2011/12

N2 - In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

AB - In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.

UR - http://hdl.handle.net/10754/561936

UR - http://arxiv.org/abs/arXiv:0811.2783v3

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M3 - Article

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JO - Nonlinear Analysis: Theory, Methods & Applications

JF - Nonlinear Analysis: Theory, Methods & Applications

IS - 18

ER -

Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

Abstract

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