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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.

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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.


25 citations in Web of Science®
22 citations in Scopus®
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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
Deposited On:17 Sep 2010 07:08
Last Modified:05 Apr 2016 13:24
Publisher:Taylor & Francis
Publisher DOI:10.1081/PDE-200040210
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2103848

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