Nonclassical shocks and the Cauchy problem for nonconvex conservation laws

D. Amadori, P. Baiti, P. G. LeFloch, B. Piccoli

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)345-372
Number of pages28
JournalJournal of Differential Equations
Issue number2
StatePublished - Jan 20 1999

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Conservation law
  • Entropy
  • Nonclassical shock
  • Weak solution

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