2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78727This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these results are indeed useful for the treatment of hybrid systems of control theory. We rely on tools forged by set-valued analysis and viability theory, which happen to be both efficient and versatile to cover many problems. They find here unexpected relevance.Dynamical Systems34K35; 34C35; 49L05; 49L25; 70H20text