Kyoto Journal of Mathematics

A simple proof of the existence of tangent bicharacteristics for noneffectively hyperbolic operators

Tatsuo Nishitani

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Abstract

The behavior of orbits of the Hamilton vector field H p of the principal symbol p of a second-order hyperbolic differential operator is discussed. In our previous paper, assuming that p is noneffectively hyperbolic on the doubly characteristic manifold Σ of p , we have proved that if H S 3 p = 0 on Σ with the Hamilton vector field H S of some specified S , then there exists a bicharacteristic landing on Σ tangentially. The aim of this paper is to provide a much more simple proof of this result since the previous proof was fairly long and rather complicated.

Article information

Source
Kyoto J. Math., Volume 55, Number 2 (2015), 281-297.

Dates
Received: 3 September 2013
Revised: 9 January 2014
Accepted: 5 March 2014
First available in Project Euclid: 11 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1433982756

Digital Object Identifier
doi:10.1215/21562261-2871758

Mathematical Reviews number (MathSciNet)
MR3356074

Zentralblatt MATH identifier
1320.35183

Subjects
Primary: 35L15: Initial value problems for second-order hyperbolic equations 35L10: Second-order hyperbolic equations
Secondary: 35L80: Degenerate hyperbolic equations

Citation

Nishitani, Tatsuo. A simple proof of the existence of tangent bicharacteristics for noneffectively hyperbolic operators. Kyoto J. Math. 55 (2015), no. 2, 281--297. doi:10.1215/21562261-2871758. https://projecteuclid.org/euclid.kjm/1433982756


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