  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.
