2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137910The recent significant enrichment of the Order Completion Method for nonlinear Systems of PDEs resulted in the global existence of generalized solutions to a large class of such equations. In this paper we investigate the existence and regularity of the generalized solutions to a family of nonlinear first order Cauchy problems. The spaces of generalized solutions are obtained as the completions of suitably constructed uniform convergence spaces.Analysis of PDEsGeneral Topology35B30; 35F10; 46A19text