On the analytic continuation of the solution of the Cauchy problem for certain differential operators of principal part with polynomial coefficients
type: Item
instance of: scholarly article
title: On the analytic continuation of the solution of the Cauchy problem for certain differential operators of principal part with polynomial coefficients
zbMATH Open document ID: 1055.35008
author: Yûsaku Hamada
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2004-08-16T00:00:00Z
review text: The author studies the domain of holomorphy of the solutions of the Cauchy problem for linear partial differential operators in Kowalewskian form. Namely, the question is whether the local holomorphy given by the Cauchy-Kowalewsky theorem can be extended to a given complex domain, cf. \textit{Y. Hamada}, \textit{J. Leray} and \textit{A. Takeuchi} [J. Math Pures Appl., IX. Sér. 64, 257--319 (1985; Zbl 0581.32017)]. Attention is here mainly fixed on the interesting two-dimensional example \[ (D_t^m-at^px^qD_x^m)u= P_{m-1}u+v, \] \[ D^k_tu(0,x)= w_k(x), \quad 0\leq k\leq m-1, \quad (t,x)\in \mathbb{C}^2, \] where \(a\in\mathbb{C}\) and \(P_{m-1}\) is a lower order operator. Assuming that the data \(v\), \(w_k\) and the coefficients of \(P_{m-1}\) are holomorphic in \(\mathbb{C}^2\), the author gives a precise study of the domain of holomorhy of the corresponding solution \(u(t,x)\).
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35A10
zbMATH DE Number: 2091871
zbMATH Keywords: domain of holomorphy
zbMATH Keywords: operators in Kowalewskian form
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113247125
OpenAlex ID: W1979757767
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DOI: 10.2748/TMJ/1113247125
description: scientific article; zbMATH DE number 2091871