ON THE EXISTENCE OF SOLUTIONS AND THE CONVERGENCE OF APPROXIMATIONS TO SCALAR CONSERVATION-LAWS

This paper deals with a new proof of the existence of weak solutions to scalar conservation laws, Our approach relies on the use of a particular finite difference scheme for time discretization which introduces a viscous term, The approximate solutions can be computed explicitly by solving a set of linear ordinary differential problems. We prove that they converge towards a weak solution which is, in a certain sense, unique and stable.