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Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws

TitleNonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws
Publication TypeJournal Article
Year of Publication1999
AuthorsAmadori, D, Baiti, P, LeFloch, PG, Piccoli, B
JournalJ. Differential Equations 151 (1999) 345-372
Abstract

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.

URLhttp://hdl.handle.net/1963/3312
DOI10.1006/jdeq.1998.3513

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