An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions

Details An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions

2003-02-19

arxiv.org/abs/math/0302227v1

Mathematics

Analysis of PDEs

12 pages, 5 figures

Scientific paper

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.

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