Preprint 2004-055

Well-Posedness for a Class of Hyperbolic Systems of Conservation Laws in Several Space Dimensions

Luigi Ambrosio, Francois 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.

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Luigi Ambrosio <>
Francois Bouchut,
Camillo De Lellis, <>
Publishing information:
To appear in Communications in Partial Differential Equations.
Submitted by:
<> October 12 2004.

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