%0 Journal Article
%D 2003
%T An ill posed Cauchy problem for a hyperbolic system in two space dimensions
%A Alberto Bressan
%X 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.
%I Università di Padova
%G en_US
%U http://hdl.handle.net/1963/2913
%1 1787
%2 Mathematics
%3 Functional Analysis and Applications
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