The multidimensional wave equation with generalized acoustic boundary conditions I: Strong stability

Zainab Abbas , Serge Nicaise (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

We study the wave equation on a domain of ℝd, d ≥ 2, with dynamical boundary control applied on a part of the boundary and a Dirichlet boundary condition on the remaining part. We prove the asymptotic stability and nonuniform stability of the associated semigroup.

Mots clés: Acoustic boundary conditions; Stability; Wave equation

Domaines: Mathématiques [math]

Zainab Abbas, Serge Nicaise. The multidimensional wave equation with generalized acoustic boundary conditions I: Strong stability. SIAM Journal on Control and Optimization, 2015, 53 (4), pp.2558-2581. ⟨10.1137/140971336⟩. ⟨hal-03134826⟩