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

Source 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.