Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T14:37:12.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Precise propagation of singularities for a hyperbolic system with characteristics of variable multiplicity

Published online by Cambridge University Press:  22 January 2016

Chisato Iwasaki  and
Yoshinori Morimoto
Chisato Iwasaki
Affiliation:
Department of Mathematics Osaka University Toyonaka, Osaka 560, Japan
Yoshinori Morimoto
Affiliation:
Department of Engineering Mathematics, Nagoya University Chikusa-ku, Nagoya 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the Cauchy problem for a hyperbolic system with characteristics of variable multiplicity and construct a certain solution whose wave front set propagates precisely along the so-called “broken null bicharacteristic flow”, in other words, along the admissible trajectory if we use the terminology of [6].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 101 , March 1986 , pp. 111 - 130
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[ 1 ] Alinhae, S., Branching of singularities for a class of hyperbolic operators, Indiana Univ. Math. J., 27 (1978), 1027–1037.Google Scholar
[ 2 ] Duistermaat, J. J., Fourier integral operators, Courant Institute of Mathematical Sciences, 1973.Google Scholar
[ 3 ] Hanges, N., Parametrices and propagation of singularities for operators with noninvolutive characteristics, Indiana Univ. Math. J., 28 (1979), 87–97.CrossRefGoogle Scholar
[ 4 ] Hörmander, L., Spectral analysis of singularities, Seminar of Singularities of Solutions of Linear Partial Differential Equations, Princeton University Press 1979, 3–49.Google Scholar
[ 5 ] Ichinose, W. and Kumanogo, H., On the propagation of singularities with infinitely many branching points for a hyperbolic equation of second order, Comm. Partial Differential Equations, 6 (1981), 568–623.CrossRefGoogle Scholar
[ 6 ] Iwasaki, C. and Morimoto, Y., Propagation of singularities of solutions for a hyperbolic system with nilpotent characteristics, I, Comm. Partial Differential Equations, 7 (1982), 743–794.CrossRefGoogle Scholar
[ 7 ] Iwasaki, C. and Morimoto, Y., Propagation of singularities of solutions for a hyperbolic system with nilpotent characteristics, II, Comm. Partial Differential Equations, 9 (1984), 1407–1436.Google Scholar
[ 8 ] Kumano-go, H., Taniguchi, K. and Tozaki, Y., Multi-product of phase functions for Fourier integral operators with an application, Comm. Partial Differential Equations, 3 (1978), 349–380.Google Scholar
[ 9 ] Kumano-go, H. and Taniguchi, K., Fourier integral operators of multi phase and the fundamental solution for a hyperbolic system, Funkcial Ekvac, 22 (1979), 161–196.Google Scholar
[10] Morimoto, Y., On the propagation of the wave front set of a solution for a hyperbolic system, Math. Japonica, 27 (1982), 501–508.Google Scholar
[11] Morimoto, Y., Propagation of wave front set in Gevrey class for an example of hyperbolic system, Nagoya Math. J., 101 (1986), 131–150.Google Scholar
[12] Taniguchi, K. and Tozaki, , A hyperbolic equation with double characteristics which has a solution with branching singularities, Math. Japonica, 25, (1980), 279–300.Google Scholar
[13] Wakabayashi, S., Singularities of solutions of the Cauchy problem for hyperbolic systems in Gevrey classes, Japan. J. Math., 11 (1985), 157–201.Google Scholar
[14] Wakabayashi, S., Singularities of solutions of the Cauchy problem for symmetric hyperbolic systems, Comm. Partial Differential Equations, 9 (1984), 1147–1177.CrossRefGoogle Scholar