Well-posedness for a class of 2 × 2 conservation laws with L data

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Abstract

The Cauchy problem for a special class of 2 × 2 systems of conservation laws with data in L1 ∩ L is considered. In the strictly hyperbolic case we prove the existence of a weak solution which depends continuously on the initial data with respect to the L1-norm. This solution can be characterized in terms of a Kružkov-type entropy condition, which is introduced here.

Original languageEnglish (US)
Pages (from-to)161-185
Number of pages25
JournalJournal of Differential Equations
Volume140
Issue number1
DOIs
Publication statusPublished - Oct 10 1997

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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