Reissig, Michael Klein-Gordon type decay rates for wave equations with a time-dependent dissipation. (English) Zbl 1002.35076 Adv. Math. Sci. Appl. 11, No. 2, 859-891 (2001). Author’s abstract: This work is concerned with the proof of decay estimates for the solutions of the Cauchy problem for the wave equation with time-dependent dissipation \(u_{tt}-\lambda ^2(t)b^2(t)\triangle u+a\lambda (t)b(t)u_{t}=0.\) Here \(\lambda=\lambda (t)\) is an increasing smooth and positive function. The positive function \(b=b(t)\) is an oscillating one. The goal is to study under which assumptions for \(\lambda\) and \(b\) one can expect decay estimates generalizing the classical result of the article by A. Matsumura [Publ. Res. Inst. Math. Sci. Kyoto Univ. 12, 169-189 (1976; Zbl 0356.35008)] for the case \(\lambda (t)\equiv 1.\) Reviewer: Marie Kopáčková (Praha) Cited in 1 Document MSC: 35L15 Initial value problems for second-order hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs Keywords:Cauchy problem; decay estimate; Klein-Gordon equation Citations:Zbl 0356.35008 PDFBibTeX XMLCite \textit{M. Reissig}, Adv. Math. Sci. Appl. 11, No. 2, 859--891 (2001; Zbl 1002.35076)