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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
67/2003

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

Luigi Ambrosio, François Bouchut and Camillo De Lellis

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.

Received:
25.07.03
Published:
25.07.03
MSC Codes:
35L45, 35L40, 35L65
Keywords:
hyperbolic systems, several dimensions, renormalized solutions

Related publications

inJournal
2004 Repository Open Access
Luigi Ambrosio, F. Bouchut and Camillo De Lellis

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

In: Communications in partial differential equations, 29 (2004) 9/10, pp. 1635-1651