In this short note we discuss the influence of a time-periodic dissipation term on a-priori estimates for solutions to dissipative wave equations. The approach is based on a diagonalisation argument for high frequencies and results from spectral theory of periodic differential equations / Floquet theory for bounded frequencies.
"On the influence of time-periodic dissipation on energy and dispersive estimates." Hiroshima Math. J. 38 (3) 397 - 410, November 2008. https://doi.org/10.32917/hmj/1233152777