Generalized uniformly continuous semigroups and semilinear hyperbolic systems with regularized derivatives

We adopt the theory of uniformly continuous operator semigroups for use in Colombeau generalized function spaces. The main objective is to find a unique solution to a class of semilinear hyperbolic systems with singularities. The idea of regularized derivatives is to transform unbounded differential operators into bounded, integral ones. This idea is used here to permit working with uniformly continuous operators.