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Creation and propagation of logarithmic singularities by interaction of two piecewise smooth progressing waves
Author(s):
G.
Laschon
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1375-1384.
MSC (2000):
Primary 35L60, 58J47
Posted:
October 20, 2000
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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:
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
Posted:
October 20, 2000
Dedicated:
Dedicated to Joanna
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2000,
American Mathematical Society
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