On the Well Posedness of a System of Balance Laws with L

Uniqueness and continuous dependence of solutions of (2) can thus be derived from the well-posedness of the Cauchy problem for (3). We remark that the genuine nonlinearity of (1) implies that the total variation of u(t0, ·) is locally bounded, for each t0 > 0. Hence the well posedness of the Cauchy problem (3) with initial data x(t0) = x0 follows from [2]. It is worth noting that in [3] the well posedness of (3) follows from a more general result on the well posedness of ODE’s of the form