2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65148We consider the Cauchy problem for the weakly dissipative wave equation $$ \bx v+\fracμ{1+t}v_t=0, \qquad x\in\R^n,\quad t\ge 0, $$ parameterized by $μ>0$, and prove a representation theorem for its solution using the theory of special functions. This representation is used to obtain $L_p$--$L_q$ estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the $L_2$ energy estimate we determine the part of the phase sp which is responsible for the decay rate. It will be shown that the situation d strongly on the value of $μ$ and that $μ=2$ is critical.29 pages, 2 figuresAnalysis of PDEs35L05; 35L15; 35B45text