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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Stratified solutions for systems of conservation laws
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by Andrea Corli and Olivier Gues PDF
Trans. Amer. Math. Soc. 353 (2001), 2459-2486 Request permission

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
  • 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.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 2459-2486
  • MSC (2000): Primary 35L65, 35L67; Secondary 35L45, 58G17
  • DOI: https://doi.org/10.1090/S0002-9947-01-02682-4
  • MathSciNet review: 1814078