A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables
type: Item
instance of: scholarly article
title: A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables
zbMATH Open document ID: 0552.35049
author: Tatsuo Nishitani
published in: Journal of Mathematics of Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: Let \(L=D^ 2_ t-A(t,x)D^ 2_ x+B(t,x)D_ x+C(t,x)D_ t+R(t,x)\) where it is assumed that the coefficients are real analytic in a neighborhood of the origin in \(R^ 2\). Consider the Cauchy problem \(Lu(t,x)=f(t,x),\) \(D^ j_ tu(t_ 0,x)=u_ j(x).\) The author gives a necessary and sufficient condition in order that the Cauchy problem stated above is \(C^{\infty}\)-well-posed.
reviewed by: N.L.Maria
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3879411
zbMATH Keywords: Cauchy problem
zbMATH Keywords: well-posed
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521387
OpenAlex ID: W1583022050
DOI: 10.1215/KJM/1250521387
description: scientific article; zbMATH DE number 3879411