A CONNECTION BETWEEN SCALAR CONSERVATION-LAWS AND INFINITE LINEAR-SYSTEMS OF PDES

We establish an explicit connection between solutions of the scalar co nservation law and infinite hyperbolic systems of linear partial diffe rential equations. As an immediate corollary of this connection combin ed with the well-known local existence theorem for the scalar conserva tion law, we obtain the corresponding local existence of smooth soluti ons for infinite linear systems. This approach also allows a way to se ek numerical solutions of scalar conservation laws via solutions of tr uncated finite linear systems of PDE's.