Necessary conditions for strong hyperbolicity of first order systems
type: Item
instance of: scholarly article
title: Necessary conditions for strong hyperbolicity of first order systems
zbMATH Open document ID: 0791.35076
DOI: 10.1007/BF02788842
author: Tatsuo Nishitani
published in: Journal d'Analyse Mathématique
publication date: 1994-07-18T00:00:00Z
review text: The author considers a first order differential operator \(L\) acting on \(C^ \infty(\Omega, \mathbb{C}^ m)\) with Cauchy data on a non- characteristic surface (where \(\Omega\) is a nonempty and open subset in \(\mathbb{R}^{n+1}\)) and gives some necessary conditions in order that \(L+B\) is correctly posed for each \(B\in C^ \infty (\Omega, M_ m(\mathbb{C}))\), i.e. that \(L\) is strongly hyperbolic. Namely, he proves that: If \(h\) and \(M=(m_{ij})\) are the determinant and the cofactor matrix of the principal symbol of \(L\) respectively, and \(L\) is strongly hyperbolic, then the Cauchy problem for \(h+m_{ij}\) is correctly posed for every \(m_{ij}\).
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35S10
zbMATH DE Number: 528674
zbMATH Keywords: strong hyperbolicity
zbMATH Keywords: strongly hyperbolic
zbMATH Keywords: first order differential operator
reviewed by: Ioan I. Vrabie
MaRDI profile type: Publication
cites work: Q5535091
cites work: Lacunas for hyperbolic differential operators with constant coefficients.I
cites work: On the singularities of solutions of partial differential equations
cites work: The Cauchy problem for differential equations with double characteristics
cites work: Q3736112
cites work: NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
cites work: Strongly hyperbolic systems with variable coefficients
cites work: Cauchy problem for non-strictly hyperbolic systems
cites work: Q3482205
cites work: Q3349302
cites work: Q3814131
cites work: Une condition nécessaire pour les systèmes hyperboliques. (A necessary condition for hyperbolic systems)
cites work: Microlocal Forms for Hyperbolic Systems
cites work: Q5343650
cites work: On holomorphically similar matrices
cites work: On the strongly hyperbolic systems. II: A reduction of hyperbolic matrices
description: scientific article; zbMATH DE number 528674