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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Multidimensional viscous shocks I: Degenerate symmetrizers and long time stability
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by Olivier Guès, Guy Métivier, Mark Williams and Kevin Zumbrun PDF
J. Amer. Math. Soc. 18 (2005), 61-120 Request permission

Abstract:

We use energy estimates to study the long time stability of multidimensional planar viscous shocks $\psi (x_1)$ for systems of conservation laws. Stability is proved for both zero mass and nonzero mass perturbations, and some of the results include rates of decay in time. Shocks of any strength are allowed, subject to an appropriate Evans function condition. The main tools are a conjugation argument that allows us to replace the eigenvalue equation by a problem in which the $x_1$ dependence of the coefficients is removed and degenerate Kreiss-type symmetrizers designed to cope with the vanishing of the Evans function for zero frequency.
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Additional Information
  • Olivier Guès
  • Affiliation: LATP, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille, France
  • Email: gues@cmi.univ-mrs.fr
  • Guy Métivier
  • Affiliation: MAB, Université de Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France
  • Email: Guy.Metivier@math.u-bordeaux.fr
  • Mark Williams
  • Affiliation: University of North Carolina, Department of Mathematics, CB 3250, Phillips Hall, Chapel Hill, NC 27599
  • MR Author ID: 225575
  • Email: williams@email.unc.edu
  • Kevin Zumbrun
  • Affiliation: Indiana University, Department of Mathematics, Rawles Hall, Bloomington, IN 47405
  • MR Author ID: 330192
  • Email: kzumbrun@indiana.edu
  • Received by editor(s): September 18, 2002
  • Published electronically: October 14, 2004
  • Additional Notes: Research was supported in part by European network HYKE grants HPRN-CT-2002-00282 (O.G.) and HPRN-CT-2002-00282 (G.M.) and by NSF grants DMS-0070684 (M.W.) and DMS-0070765 (K.Z.).
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 18 (2005), 61-120
  • MSC (2000): Primary 35L60; Secondary 35B35, 35B45, 35K55, 35L65, 76L05
  • DOI: https://doi.org/10.1090/S0894-0347-04-00470-9
  • MathSciNet review: 2114817