A connection between scalar conservation laws and infinite linear systems of PDE's

Abstract

We establish an explicit connection between solutions of the scalar conservation law and infinite hyperbolic systems of linear partial differential equations. As an immediate corollary of this connection combined with the well-known local existence theorem for the scalar conservation law, we obtain the corresponding local existence of smooth solutions for infinite linear systems. This approach also allows a way to seek numerical solutions of scalar conservation laws via solutions of truncated finite linear systems of PDE's.