Necessary conditions for hyperbolic systems
type: Item
instance of: scholarly article
title: Necessary conditions for hyperbolic systems
zbMATH Open document ID: 1029.35163
DOI: 10.1016/S0007-4497(02)01122-3
author: Antonio Bove
author: Tatsuo Nishitani
published in: Bulletin des Sciences Mathématiques
publication date: 2003-03-23T00:00:00Z
review text: This paper deals with the Cauchy problem for first order hyperbolic system \(L(x,{\mathcal D})\) having characteristic points of higher multiplicity. In other words, the determinant of the principal symbol has multiple characteristic points. The authors consider the case when at a multiple characteristic point the principal symbol of the system has corank 2. The main aim here is to obtain general necessary conditions for the \(C^\infty\) well posedness of the Cauchy problem. These conditions involve a suitably defined determinant \(\text{Det}_{(s)}\) of the full symbol of \(L\). The method of the proof consists in constructing of an asymptotic null solution which violates an a priori estimate resulting from the \(C^\infty\) well posedness of the Cauchy problem.
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 1886860
zbMATH Keywords: hyperbolic systems
zbMATH Keywords: multiple characteristics
zbMATH Keywords: Cauchy problem
zbMATH Keywords: necessary
zbMATH Keywords: conditions for well-posedness
zbMATH Keywords: noncommutative determinant
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
cites work: Q3241211
cites work: The Cauchy problem for hyperbolic systems with multiple characteristics
cites work: Q4467756
cites work: Q4763149
cites work: Les déterminants sur un corps non commutatif
cites work: NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
cites work: Q4831641
cites work: Hyperbolicity of localizations
cites work: Strongly hyperbolic systems of maximal rank
cites work: Necessary conditions for strong hyperbolicity of first order systems
cites work: The determinant of matrices of pseudo-differential operators
description: scientific article; zbMATH DE number 1886860