Generalized solutions to singular initial-boundary hyperbolic problems with non-Lipshitz nonlinearities

Abstract

We prove the existence and uniqueness of global generalized solutions in a Colombeau algebra of generalized functions to semilinear hyperbolic systems with nonlinear boundary conditions. Our analysis covers the case of non-Lipschitz nonlinearities both in the differential equations and in the boundary conditions. We admit strong singularities in the differential equations as well as in the initial and boundary conditions. AMS Mathematics Subject Classification (2000): 35L50, 35L67, 35D05.