Initial-Boundary Problems for Semilinear Hyperbolic Systems with Singular Coefficients

摘要

We use the framework of Colombeau algebras of generalized functions to studyexistence and uniqueness of global generalized solutions to mixed non-localproblems for a semilinear hyperbolic system. Coefficients of the system as wellas initial and boundary data are allowed to be strongly singular, as the Diracdelta function and derivatives thereof. To obtain the existence-uniquenessresult we prove a criterion of invertibility in the full version of theColombeau algebras.