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

Gerbi, Stéphane; Said-Houari, Belkacem

Type

Article

Authors

Gerbi, Stéphane
Said-Houari, Belkacem

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Date

2011-12

Preprint Posting Date

2008-11-17

Permanent link to this record

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

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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. © 2011 Elsevier Ltd. All rights reserved.

Citation

Gerbi, S., & Said-Houari, B. (2011). Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions. Nonlinear Analysis: Theory, Methods & Applications, 74(18), 7137–7150. doi:10.1016/j.na.2011.07.026