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

2003/02/19 by Alberto Bressan, Bressan, Alberto · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0302227

12 pages, 5 figures

arxiv created 2003/02/19 · arxiv updated 2009/11/30

Abstract

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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