Initial-Boundary Problems for Semilinear Hyperbolic Systems with Singular Coefficients

Abstract

We use the framework of Colombeau algebras of generalized functions to study existence and uniqueness of global generalized solutions to mixed non-local problems for a semilinear hyperbolic system. Coefficients of the system as well as initial and boundary data are allowed to be strongly singular, as the Dirac delta function and derivatives thereof. To obtain the existence-uniqueness result we prove a criterion of invertibility in the full version of the Colombeau algebras.