Stabilization of the Wave Equations with Potential and Indefinite Damping

Kangshen Liu , Bopeng Rao (1) , Xu Zhang

1 IRMA - Institut de Recherche Mathématique Avancée

By means of global Carleman-type estimate, we study the stabilization problem of the wave equations with potential and indefinite damping. The energy decay rate of the system is given explicitly. Also, we obtain an upper bound estimate on the negative damping to guarantee the energy of the system decays exponentially.

Mots clés: "Stabilization; energy decay rate; wave equation; indefinite damping; observability inequality; Carleman estimate."; Stabilization; Carleman estimate

Domaines: Optimisation et contrôle [math.OC]

Kangshen Liu, Bopeng Rao, Xu Zhang. Stabilization of the Wave Equations with Potential and Indefinite Damping. 2002. ⟨hal-00129676⟩