Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping

Abstract

Synopsis This report deals with the asymptotic behaviour of solutions of the wave equation in a domain Ω ⊆ R n . The boundary, Γof Ωft consists of two parts. One part reflects all energy while the other part absorbs energy to a degree. If the energy-absorbing part is non-empty we show that the energy tends to zero as t →∞. With stronger assumptions we are able to obtain decay rates for the energy. Certain relationships with controlability are discussed and used to advantage.