Abstract:We give an example of a Cauchy problem for a nonlinear hyperbolic system of conservation laws in two space dimension which is not well posed. A sequence of initial data in L^infty converges strongly, but the sequence of solutions has no strong limit, due to oscillation phoenomena. The weak limit fails to be a weak solution, in general.

**Paper:**- Available as PostScript (224 Kbytes) or gzipped PostScript (78 Kbytes; uncompress using gunzip).
**Author(s):**- Alberto Bressan, <bressan@sissa.it>
**Publishing information:**- To appear on: Rendiconti del Seminario matematico, Universita' di Padova.
**Comments:****Submitted by:**- <bressan@sissa.it> February 12 2003.

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Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Thu Feb 13 09:31:09 MET 2003