UZH-Logo

Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions


Ambrosio, L; Bouchut, F; De Lellis, C (2004). Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. Communications in Partial Differential Equations, 29(9-10):1635-1651.

Abstract

In this paper we consider a system of conservation laws in several space dimensions whose nonlinearity is due only to the modulus of the solution. This system, first considered by Keyfitz and Kranzer in one space dimension, has been recently studied by many authors. In particular, using standard methods from DiPerna-Lions theory, we improve the results obtained by the first and third author, showing existence, uniqueness and stability results in the class of functions whose modulus satisfies, in the entropy sense, a suitable scalar conservation law. In the last part of the paper we consider a conjecture on renormalizable solutions and show that this conjecture implies another one recently made by Bressan in connection with the system of Keyfitz and Kranzer.

In this paper we consider a system of conservation laws in several space dimensions whose nonlinearity is due only to the modulus of the solution. This system, first considered by Keyfitz and Kranzer in one space dimension, has been recently studied by many authors. In particular, using standard methods from DiPerna-Lions theory, we improve the results obtained by the first and third author, showing existence, uniqueness and stability results in the class of functions whose modulus satisfies, in the entropy sense, a suitable scalar conservation law. In the last part of the paper we consider a conjecture on renormalizable solutions and show that this conjecture implies another one recently made by Bressan in connection with the system of Keyfitz and Kranzer.

Citations

25 citations in Web of Science®
22 citations in Scopus®
Google Scholar™

Altmetrics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Hyperbolic systems; Several dimensions; Renormalized solutions
Language:English
Date:2004
Deposited On:17 Sep 2010 07:08
Last Modified:05 Apr 2016 13:24
Publisher:Taylor & Francis
ISSN:0360-5302
Publisher DOI:10.1081/PDE-200040210
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2103848

Download

Full text not available from this repository.View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations