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

Stéphane Gerbi (1) , Belkacem Said-Houari (2)

1 LAMA - Laboratoire de Mathématiques
2 UBMA - Université Badji Mokhtar [Annaba]

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.

Mots clés: dynamic boundary conditions; Damped wave equations; stable and unstable set; global solutions; blow up; Kelvin-Voigt damping; dynamic boundary conditions.

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Gerbi, Belkacem Said-Houari. Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions.. Nonlinear Analysis: Theory, Methods and Applications, 2011, 74 (18), pp.7137-7150. ⟨10.1016/j.na.2011.07.026⟩. ⟨hal-00339258v3⟩