Exchange of conserved quantities in nonhyperbolic systems-an example

The velocity function associated with a smooth solution of "zero pressure gas dynamics" satisfies Burgers equation. Indeed an elementary generalization holds for scalar conservation laws. Weak solutions, however, are compatible in this respect only under special conditions on the initial density function. Our result depends on the uniform convexity of the flux function associated with the scalar equation, and on the entropy condition applied to both systems.