Energy decay rate of wave equations with indefinite damping.

Ahmed Benaddi (1) , Bopeng Rao (1)

1 IRMA - Institut de Recherche Mathématique Avancée

"We consider the one-dimensional wave equation with an indefinite sign damping and a zero order potential term. Using a shooting method, we establish the asymptotic expansion of eigenvalues and eigenvectors of the damped wave equation for a large class of coefficients. In addition, if the damping coefficient is "more positive than negative", we prove that the energy of system decays uniformly exponentially to zero. This generalizes a previous work of Freitas and Zuazua (1996). "

Mots clés: "indefinite damping; spectrum expansion; Riesz basis; exponential decay rate"; indefinite damping; exponential decay rate

Domaines: Equations aux dérivées partielles [math.AP]

Ahmed Benaddi, Bopeng Rao. Energy decay rate of wave equations with indefinite damping.. 1999. ⟨hal-00129628⟩