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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Creation and propagation of logarithmic singularities by interaction of two piecewise smooth progressing waves


Author: G. Laschon
Journal: Proc. Amer. Math. Soc. 129 (2001), 1375-1384
MSC (2000): Primary 35L60, 58J47
Published electronically: October 20, 2000
MathSciNet review: 1814163
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05813-5
PII: S 0002-9939(00)05813-5
Keywords: Microlocal analysis, conormal singularities, semi-linear interaction
Received by editor(s): July 22, 1999
Published electronically: October 20, 2000
Dedicated: Dedicated to Joanna
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society