Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Stratified solutions for systems of conservation laws


Authors: Andrea Corli and Olivier Gues
Journal: Trans. Amer. Math. Soc. 353 (2001), 2459-2486
MSC (2000): Primary 35L65, 35L67; Secondary 35L45, 58G17
Published electronically: February 13, 2001
MathSciNet review: 1814078
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Abstract:

We study a class of weak solutions to hyperbolic systems of conservation (balance) laws in one space dimension, called stratified solutions. These solutions are bounded and ``regular'' in the direction of a linearly degenerate characteristic field of the system, but not in other directions. In particular, they are not required to have finite total variation. We prove some results of local existence and uniqueness.


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Additional Information

Andrea Corli
Affiliation: Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy
Email: crl@dns.unife.it

Olivier Gues
Affiliation: Laboratoire J.-A. Dieudonné, UMR 6621 CNRS, Université de Nice - Sophia Antipolis, 06108 Nice, cedex 2, France
Email: gues@unice.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02682-4
Keywords: Hyperbolic systems of conservation laws, linearly degenerate eigenvalue, weak solutions, stratified solutions
Received by editor(s): April 7, 1999
Received by editor(s) in revised form: January 7, 2000
Published electronically: February 13, 2001
Additional Notes: This research was performed at the “Laboratoire J. A. Dieudonné” of the University of Nice while the first author was a recipient of an Italian CNR grant, and at the University of Ferrara, which the second author thanks for its hospitality.
Article copyright: © Copyright 2001 American Mathematical Society