Calculus of Variations and Geometric Measure Theory

L. Ambrosio - F. Bouchut - C. De Lellis

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

created on 25 Jul 2003
modified by delellis on 05 May 2011


Published Paper

Inserted: 25 jul 2003
Last Updated: 5 may 2011

Journal: Comm. Partial Differential Equations
Volume: 29
Number: 9--10
Pages: 1635-1671
Year: 2004


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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Keywords: Hyperbolic systems, several space dimensions, rerenormalized solutions