  The 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.
