David Seifert (Newcastle University)

Resolvent estimates and rates of decay of operator semigroups

Abstract:
For some time now there has been considerable interest, often motivated by applications to the study of energy decay of damped waves, in results which allow one to convert a resolvent estimate for a semigroup generator into a rate of decay for the associated semigroup. In this talk I shall survey some of the main results in this area, including a recent optimal result in the Hilbert space setting. If time permits I may also outline an abstract approach to obtaining resolvent estimates for a general class of second-order systems which can be used to study not only damped waves but also damped (fractional) Klein-Gordon equations and damped beam equations. The talk is based on joint work with Ralph Chill, Lassi Paunonen, Jan Rozendaal, Reinhard Stahn and Yuri Tomilov.