On the strongly hyperbolic systems
type: Item
instance of: scholarly article
title: On the strongly hyperbolic systems
zbMATH Open document ID: 0658.35059
author: Hideo Yamahara
published in: Journal of Mathematics of Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: Let be \[ Lu:=\partial_ tu-\sum^{n}_{k=1}A_ k(x,t)\partial_{x_ k}u, \] where u is an m-vector and \(A_ k\) are \(m\times m\)-matrices in \(C^{\infty}({\mathbb{R}}^ n_ x\times (-T,T))\). The author proves the following theorem: Assume that there exist \((x_ 0,t_ 0;\xi^ 0)\in {\mathbb{R}}^ n_ x\times (-T,T)\times {\mathbb{R}}^ n_{\xi}\setminus \{0\}\) and \(\lambda^ 0\in {\mathbb{R}}\) such that \(rank(\lambda^ 0I-\sum^{n}_{k=1}A_ k(x_ 0,t_ 0)\xi^ 0_ k)=m-1.\) Then in order that L is a strongly hyperbolic system, it is necessary that the multiplicity of the characteristic root \(\lambda^ 0\) must be less than 3. This result shows that an assumption in a theorem of \textit{T. Nishitani} [Proc. Japan Acad., Ser. A 61, 193-196 (1985; Zbl 0579.35046)] is natural.
Mathematics Subject Classification ID: 35L40
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 4075658
zbMATH Keywords: strongly hyperbolic
zbMATH Keywords: multiplicity of the characteristic root
reviewed by: Wolfgang Watzlawek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520717
OpenAlex ID: W1509339368
DOI: 10.1215/KJM/1250520717
description: scientific article; zbMATH DE number 4075658