Preprint 2003-013

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

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.

Paper:

Available as PostScript (224 Kbytes) or gzipped PostScript (78 Kbytes; uncompress using gunzip).

Author(s):

Alberto Bressan, <bressan@sissa.it>

Publishing information:

To appear on: Rendiconti del Seminario matematico, Universita' di Padova.

Comments:

Submitted by:

<bressan@sissa.it> February 12 2003.