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Well-posedness for a class of hyperbolic systems of conservation laws in several space dimensions. (English) Zbl 1072.35116
Authors’ abstract: 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.

MSC:
35L65 Hyperbolic conservation laws
35L45 Initial value problems for first-order hyperbolic systems
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