Generalized solutions of first order nonlinear Cauchy problems

In this paper, we show how the Order Completion Method for systems of nonlinear partial differential equations may be applied to solve first order initial value problems. In particular, we construct generalized solutions of a large family of such initial value problems in two related spaces of generalized functions. The way in which the two mentioned solution concepts relate to each other is discussed, as well as the basic regularity properties of solutions.