2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143538This paper proves the local well posedness of differential equations in metric spaces under assumptions that allow to comprise several different applications. We consider below a system of balance laws with a dissipative non local source, the Hille-Yosida Theorem, a generalization of a recent result on nonlinear operator splitting, an extension of Trotter formula for linear semigroups and the heat equation.25 pagesDynamical SystemsAnalysis of PDEs34G20; 47J35; 35L65text