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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Creation and propagation of logarithmic singularities by interaction of two piecewise smooth progressing waves
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by G. Laschon PDF
Proc. Amer. Math. Soc. 129 (2001), 1375-1384 Request permission

Abstract:

Our aim is to understand the non-conservation of the piecewise smooth regularity by a semi-linear interaction of two transverse progressing waves. Indeed, we know that this phenomenon occurs when the number of characteristic hypersurfaces passing through the locus of interaction, that is, a two-codimensional variety, is strictly inferior to the size of the considered first order strictly hyperbolic system. Thanks to the study of a significant example, we explain the obstruction to the piecewise smooth propagation by a loss of transmission property for the symbols describing the conormal singularities, which originates logarithmic singularities.
References
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Additional Information
  • G. Laschon
  • Affiliation: Laboratoire J.A. Dieudonné, Université Nice-Sophia Antipolis, Parc Valrose, F06108 Nice cedex 2, France
  • Address at time of publication: Institut de Recherche Mathématique de Rennes, Université Rennes 1, Campus de Beaulieu, F35042 Rennes cedex, France
  • Email: laschon@maths.univ-rennes1.fr
  • Received by editor(s): July 22, 1999
  • Published electronically: October 20, 2000

    • Dedicated: Dedicated to Joanna
  • Communicated by: David S. Tartakoff
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 1375-1384
  • MSC (2000): Primary 35L60, 58J47
  • DOI: https://doi.org/10.1090/S0002-9939-00-05813-5
  • MathSciNet review: 1814163