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

55 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

Access to Document

10.1006/jdeq.1997.3308

Cite this

@article{4522c9afbd7c47c98671889d2d9f1845,

title = "Well-posedness for a class of 2 × 2 conservation laws with L∞ data",

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.",

author = "Paolo Baiti and Jenssen, \{Helge Kristian\}",

year = "1997",

month = oct,

day = "10",

doi = "10.1006/jdeq.1997.3308",

language = "English (US)",

volume = "140",

pages = "161--185",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Well-posedness for a class of 2 × 2 conservation laws with L∞ data

AU - Baiti, Paolo

AU - Jenssen, Helge Kristian

PY - 1997/10/10

Y1 - 1997/10/10

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0031563744

UR - https://www.scopus.com/inward/citedby.url?scp=0031563744&partnerID=8YFLogxK

U2 - 10.1006/jdeq.1997.3308

DO - 10.1006/jdeq.1997.3308

M3 - Article

AN - SCOPUS:0031563744

SN - 0022-0396

VL - 140

SP - 161

EP - 185

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this