Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes
type: Item
instance of: scholarly article
title: Cauchy problems for Fuchsian hyperbolic equations in spaces of functions of Gevrey classes
zbMATH Open document ID: 0586.35060
author: Hidetoshi Tahara
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: This note deals with the Cauchy problem \[ t^ k \partial^ m_ t u+\sum t^{p(j,\alpha)} a_{j,\alpha} \partial^ j_ t \partial_ x^{\alpha} u=f(t,x),\quad \partial^ i_ t u(0,x)=u_ i(x), \] i\(=0,1,...,m-k-1\), \(0\leq t\leq T\), \(x\in {\mathbb{R}}^ n\), where m, k are integers, \(0\leq k<m\), \(0\leq p(j,\alpha)\) suitable integers, \(j+| \alpha | \leq m\), \(j<m\), with suitable hyperbolicity conditions. The problem is well posed in spaces of \(C^{\infty}\) functions and in spaces of functions of Gevrey classes. Moreover the solution has finite propagation speed.
Mathematics Subject Classification ID: 35L30
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 58J47
zbMATH DE Number: 3939855
zbMATH Keywords: Fuchsian hyperbolic equations
zbMATH Keywords: Cauchy problem
zbMATH Keywords: hyperbolicity conditions
zbMATH Keywords: Gevrey classes
zbMATH Keywords: finite propagation speed
MaRDI profile type: Publication
full work available at URL: pjaa.61.63
OpenAlex ID: W1974970024
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cites work: Conditions for well-posedness in Gevrey classes of the Cauchy problems for Fuchsian hyperbolic operators
DOI: 10.3792/PJAA.61.63
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description: scientific article; zbMATH DE number 3939855