00871nas a2200109   4500008004300000245008000043210006900123260002600192520048600218100002100704856003600725       2003                        en_Ud  00aAn ill posed Cauchy problem for a hyperbolic system in two space dimensions0 aill posed Cauchy problem for a hyperbolic system in two space di  bUniversità di Padova3 aThe theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed.1 aBressan, Alberto  uhttp://hdl.handle.net/1963/2913