Preprint 2003-013

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

Alberto Bressan

Abstract: We give an example of a Cauchy problem for a nonlinear hyperbolic system of conservation laws in two space dimension which is not well posed. A sequence of initial data in L^infty converges strongly, but the sequence of solutions has no strong limit, due to oscillation phoenomena. The weak limit fails to be a weak solution, in general.

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Alberto Bressan, <>
Publishing information:
To appear on: Rendiconti del Seminario matematico, Universita' di Padova.
Submitted by:
<> February 12 2003.

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