2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68220We consider the Cauchy problem for a hyperbolic pseudodifferential operator whose symbol is generalized, resembling a representative of a Colombeau generalized function. Such equations arise, for example, after a reduction-decoupling of second-order model systems of differential equations in seismology. We prove existence of a unique generalized solution under log-type growth conditions on the symbol, thereby extending known results for the case of differential operators with generalized functions as coefficients.Analysis of PDEsFunctional Analysis46F30; 35S10text