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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:
Jul 25, 2003
Published:
Jul 25, 2003
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