Characterizations of the well posed Cauchy problem for a system in a complex domain
type: Item
instance of: scholarly article
title: Characterizations of the well posed Cauchy problem for a system in a complex domain
zbMATH Open document ID: 0742.35004
author: Masatake Miyake
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1992-06-25T00:00:00Z
review text: The paper contains interesting results on the problem of wellposedness of the Cauchy problem for systems of linear partial differential equations with holomorphic coefficients. The first paragraph of the author's introduction gives a good survey of the contents: ``The purpose of this paper is to characterize the well posed Cauchy problem for a system of linear partial differential equations in a complex domain. In particular, one of our interests is to investigate matrices of linear partial differential operators normalizable in the time derivative, and another one is to show the necessity of non-characteristicness of the initial hyperplane for the well posed Cauchy problem. For that purpose the determinant theory for matrices of linear partial differential operators due to \textit{M. Sato} and \textit{M. Kashiwara} [Proc. Japan Acad. 51, 17-19 (1975; Zbl 0337.35067)] plays an important role. In particular, characterizations of invertible matrices, which will be given in Section 2, play the most crucial role.'' Among the papers which were important for the development of the theory we also mention a paper of \textit{T. Sadamatsu} [J. Math. Kyoto Univ. 24, 593-609 (1984; Zbl 0575.35002)].
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 6631
zbMATH Keywords: characteristics
zbMATH Keywords: wellposedness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: systems of linear partial differential equations
zbMATH Keywords: holomorphic coefficients
zbMATH Keywords: matrices of linear partial differential operators normalizable in the time derivative
zbMATH Keywords: determinant theory for matrices
zbMATH Keywords: characterizations of invertible matrices
reviewed by: Wolfgang Watzlawek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227656
OpenAlex ID: W2080813819
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DOI: 10.2748/TMJ/1178227656
description: scientific article; zbMATH DE number 6631