Abstract: We consider the Cauchy problem for $n\times n$ strictly hyperbolic systems of balance lawsu_t+f(u)_x=g(x,u), x \in R, t>0\\ u(0,.)=u_0 \in L^1 \cap {\bf BV}(R; R^n), \\ |\lambda_i(u)| \geq c > 0 for all i\in \{1,\ldots,n\}, \\ |g(.,u)|+|\nabla_u g(.,u)|\leq \omega \in L^1\cap L^\infty(R),each characteristic field being genuinely nonlinear or linearly degenerate. Assuming that $\|\omega\|_{L^1(R)}$ and $\|u_o\|_{{\bf BV}(R)}$ are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation as limits of special wave-front tracking approximations. Moreover, we give a characterization of the semigroup trajectories in terms of integral estimates.
Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Tue Dec 12 14:03:22 MET 2000