TY - JOUR
T1 - Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws
JF - J. Differential Equations 151 (1999) 345-372
Y1 - 1999
A1 - Debora Amadori
A1 - Paolo Baiti
A1 - Philippe G. LeFloch
A1 - Benedetto Piccoli
AB - 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/3312
U1 - 1018
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -