01145nas a2200145 4500008004300000245007900043210006900122260001300191520067400204100002000878700001700898700002500915700002300940856003600963 1999 en_Ud 00aNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws0 aNonclassical Shocks and the Cauchy Problem for Nonconvex Conserv bElsevier3 aThe 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.1 aAmadori, Debora1 aBaiti, Paolo1 aLeFloch, Philippe G.1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/3312