$L^p$--$L^q$ decay estimates for wave equations with monotone time-dependent dissipation

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172415This expository article is intended to give an overview about recently achieved results on asymptotic properties of solutions to the Cauchy problem $u_{tt}-Δu+b(t)u_t =0,\qquad u(0,\cdot)=u_1,\quad \mathrm{D}_tu(0,\cdot)=u_2$ for a wave equation with time-dependent dissipation term. The results are based on structural properties of the Fourier multipliers representing its solution. The article explains the general philosophy behind the approach.15 pages, 2 figuresAnalysis of PDEs35L15; 35B45; 34E20$L^p$--$L^q$ decay estimates for wave equations with monotone time-dependent dissipationtext