The Cauchy problem for effectively hyperbolic equations (a special case)
type: Item
instance of: scholarly article
title: The Cauchy problem for effectively hyperbolic equations (a special case)
zbMATH Open document ID: 0546.35037
author: Nobuhisa Iwasaki
published in: Journal of Mathematics of Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: This paper is the first step to prove the proposition that effectively hyperbolic operators are strongly hyperbolic. (The converse has been proved by V. Ya. Ivrij and V. Petkov.) Here it is proved by the factorization method that the Cauchy problem for a hyperbolic equation of second order is well posed if it satisfies an assumption. It will be shown in a forthcoming paper for the standard type of the problem in the title [Publ. Res. Inst. Math. Sci. 20 (1984) (to appear)], that any effectively hyperbolic operator of second order satisfies this assumption. The last part of this work (to appear) deals with the general case to complete the proposition for single equations of higher order by reduction to the previous cases and to extend it to non-linear equations by means of the Nash-Moser implicit function theorem. [Refer to RIMS Kokyuroku 468, Kyoto Univ. (1984), or to a note by the author in Proc. Symp. Pure Math. (1983) on Nonlinear Functional Analysis and Applications.]
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3869838
zbMATH Keywords: effectively hyperbolic operators
zbMATH Keywords: strongly hyperbolic
zbMATH Keywords: factorization method
zbMATH Keywords: Cauchy problem
zbMATH Keywords: well posed
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521480
OpenAlex ID: W1482116893
DOI: 10.1215/KJM/1250521480
description: scientific article; zbMATH DE number 3869838