Abstract:We consider the Cauchy problem for the $2\times 2$ nonstrictly hyperbolic systemFor possibly large, discontinuous and resonant data, the generalized solution to the Riemann problem is introduced, interaction estimates are carried out using a new change of variables and the convergence of Godunov approximations is shown. Uniqueness is addressed relying on a suitable extension of Kru\v zkov's techniques.

a _{t}=0,(a,u)(0,\cdot)=(a _{o},u_{o}).u _{t}+f(a,u)_{x}- g(a,u)a_{x}=0,

**Paper:**- Available as PostScript (616 Kbytes) or gzipped PostScript (224 Kbytes; uncompress using gunzip).
**Author(s):**- Debora Amadori, <amadori@univaq.it>
- Laurent Gosse, <l.gosse@area.ba.cnr.it>
- Graziano Guerra, <graziano.guerra@unimib.it>
**Publishing information:****Comments:****Submitted by:**- <graziano.guerra@unimib.it> February 17 2003.

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