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December 2020 Transversally strictly hyperbolic systems
Tatsuo Nishitani
Kyoto J. Math. 60(4): 1399-1418 (December 2020). DOI: 10.1215/21562261-2019-0066

Abstract

We consider the Cauchy problem for first-order systems. Assuming that the set Σ of singular points of the characteristic variety is a smooth manifold and the characteristic values are real and semisimple, we introduce a new class which is strictly hyperbolic in the directions transverse to Σ . If the propagation cone and Σ are compatible, we prove, under some additional conditions, that transversally strictly hyperbolic systems are strongly hyperbolic. On the other hand, if the propagation cone is incompatible with Σ , then transversally strictly hyperbolic systems are much more involved, which is discussed utilizing an interesting example.

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Tatsuo Nishitani. "Transversally strictly hyperbolic systems." Kyoto J. Math. 60 (4) 1399 - 1418, December 2020. https://doi.org/10.1215/21562261-2019-0066

Information

Received: 18 December 2017; Revised: 29 July 2018; Accepted: 11 December 2018; Published: December 2020
First available in Project Euclid: 6 October 2020

MathSciNet: MR4175813
Digital Object Identifier: 10.1215/21562261-2019-0066

Subjects:
Primary: 35L45
Secondary: 35F40

Rights: Copyright © 2020 Kyoto University

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Vol.60 • No. 4 • December 2020
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