Local existence and exponential growth 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 damped semiliear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined with a contraction mapping theorem. Secondly, the exponential growth of the energy and the $L^p$ norm of the solution is presented.

Mots clés: Damped wave equations; Kelvin-Voigt damping; dynamic boundary conditions; local existence; Faedo-Galerkin approximation; exponential growth

Domaines: Equations aux dérivées partielles [math.AP]

Stéphane Gerbi, Belkacem Said-Houari. Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions. Advances in Differential Equations, 2008, 13 (11-12), pp.1051-1074. ⟨hal-00326862⟩