%0 Journal Article
%J J. Differential Equations 151 (1999) 345-372
%D 1999
%T Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws
%A Debora Amadori
%A Paolo Baiti
%A Philippe G. LeFloch
%A Benedetto Piccoli
%X The Riemann problem for a conservation law with a nonconvex (cubic) flux can be solved in a class of admissible nonclassical solutions that may violate the Oleinik entropy condition but satisfy a single entropy inequality and a kinetic relation. We use such a nonclassical Riemann solver in a front tracking algorithm, and prove that the approximate solutions remain bounded in the total variation norm. The nonclassical shocks induce an increase of the total variation and, therefore, the classical measure of total variation must be modified accordingly. We prove that the front tracking scheme converges strongly to a weak solution satisfying the entropy inequality.
%B J. Differential Equations 151 (1999) 345-372
%I Elsevier
%G en_US
%U http://hdl.handle.net/1963/3312
%1 1018
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-20T11:49:26Z\\nNo. of bitstreams: 1\\nNonclassical_shocks.pdf: 261875 bytes, checksum: bd41bb6490895996b965941b1eeb6797 (MD5)
%R 10.1006/jdeq.1998.3513