L_p − L_q Decay Estimates for Wave Equations with Time-Dependent Coefficients

Abstract

The goal of this survey article is to explain the up-to-date state of the theory of L_p − L_q decay estimates for wave equations with time-dependent coefficients. We explain the influence of oscillations in the coefficients by using a precise classification. Moreover, we will see how mass and dissipation terms take influence on the L_p − L_q decay estimates.