D. Chae et P. Dubovskii, A CONNECTION BETWEEN SCALAR CONSERVATION-LAWS AND INFINITE LINEAR-SYSTEMS OF PDES, Applied mathematics letters, 8(5), 1995, pp. 21-25
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.