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

Paolo Baiti; Helge Kristian Jenssen

doi:10.1006/jdeq.1997.3308

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

Paolo Baiti, Helge Kristian Jenssen

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

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 language	English (US)
Pages (from-to)	161-185
Number of pages	25
Journal	Journal of Differential Equations
Volume	140
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1997.3308
State	Published - Oct 10 1997

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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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 Kru{\v z}kov-type entropy condition, which is introduced here.",

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