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arXiv · 0811.2783

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

Stéphane Gerbi·Belkacem Said-Houari
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Abstract

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt 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.

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Stéphane Gerbi, Belkacem Said-Houari. 2008-11-17. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions. https://doi.org/10.1016/j.na.2011.07.026

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