Large-data solution of a model system for singular shocks

A suitably modified front-tracking algorithm is used to solve a class of Cauchy problems for a pair of conservation laws known as the model system for singular shocks or as the KeyfitzKranzer system. Initial data of large oscillation and including a finite number of positive Dirac masses in one of the dependent variables is permitted. For such initial data, a distribution solution is constructed up to an arbitrary given finite time T. At any given time up to T, the constructed solution is uniformly bounded in space except possibly at a finite number of points. With respect to time, our solutions are weakly Lipshitz in the space of measures on . However, our solutions are not traditional weak solutions, because of the unavoidable appearance of singular shocks carrying finite Dirac mass. Furthermore, the bounded parts of our solutions are of lower than customary regularity, being of bounded 2-variation in space, pointwise but not uniformly with respect to time.