The Cauchy problem for a class of hyperbolic operators with triple characteristics
type: Item
instance of: scholarly article
title: The Cauchy problem for a class of hyperbolic operators with triple characteristics
zbMATH Open document ID: 0687.35053
author: Enrico Bernardi
author: Antonio Bove
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: The author gives both a necessary condition and a sufficient condition for \(C^{\infty}\)-wellposedness of the Cauchy problem for a class of hyperbolic operators with triple characteristic. In comparison with the involutive or effectively hyperbolic case the above both conditions contain the so called Levi conditions imposed on the subprincipal symbol \(P^ s_{m-1}(x,\xi)\). The sufficient condition contains Ivrii-Petkov- Hörmander condition, and the necessary condition contains Ivrii-Petkov condition as special cases.
Mathematics Subject Classification ID: 35L30
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 4125930
zbMATH Keywords: triple characteristics
zbMATH Keywords: wellposedness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Levi conditions
zbMATH Keywords: subprincipal symbol
reviewed by: Akira Tsutsumi
MaRDI profile type: Publication
full work available at URL: pjaa.64.364
OpenAlex ID: W2031962097
cites work: Propagation of singularities for hyperbolic operators with multiple involutive characteristics
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cites work: Q3736112
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cites work: NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
cites work: Hyperbolic operators with symplectic multiple characteristics
cites work: Singularities of solutions of the caught problem for symmetric hyperbolic systems
DOI: 10.3792/PJAA.64.364
description: scientific article; zbMATH DE number 4125930