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.

**Paper:**- Available as PostScript (485 Kbytes) or gzipped PostScript (182 Kbytes; uncompress using gunzip).
**Author(s):**- Debora Amadori, <Debora.Amadori@mat.unimi.it>
- Laurent Gosse, <laurent@mailhost.univaq.it>
- Graziano Guerra, <graziano.guerra@unimib.it>
**Publishing information:****Comments:****Submitted by:**- <graziano.guerra@unimib.it> December 11 2000.

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