Cm-theory of damped wave equations with stabilisation

The aim of this note is to extend the energy decay estimates from [J. Wirth, Wave equations with time-dependent-dissipation. I: Non-effective dissipation, J. Differential Equations 222 (2006) 487–514] to a broader class of time-dependent dissipation including very fast oscillations. This is achieved using stabilisation conditions on the coefficient in the spirit of [F. Hirosawa, On the asymptotic behavior of the energy for wave equations with time-depending coefficients, Math. Ann. 339 (4) (2007) 819–839]. © 2008 Elsevier Inc. All rights reserved.