A remark on the \(C^ \infty\)-Goursat problem. II
type: Item
instance of: scholarly article
title: A remark on the \(C^ \infty\)-Goursat problem. II
zbMATH Open document ID: 0798.35030
author: Yukiko Hasegawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1994-10-30T00:00:00Z
review text: The author continues his research from [J. Math. Kyoto Univ. 28, No. 1, 37-51 (1988; Zbl 0701.35050)] on the \(C^ \infty\)-Goursat problem for partial differential operators with constant coefficients of the type \[ L= \sum_{i+j+|\alpha|\leq m} a_{ij\alpha} \partial^ i_ t \partial^ j_ x \partial^ \alpha_ y,\quad t\geq 0,\quad x\in\mathbb{R},\quad y\in \mathbb{R}^ n \] with \[ a_{ij\alpha}=0\quad\text{ for } i+ j+|\alpha|= m,\;i>m- r:=s\quad\text{ and }\sum_{j+| \alpha|= r} a_{sj\alpha} \xi^ j \mu^ \alpha\neq 0. \] The main result says: If the Goursat problem is \(\varepsilon\)-well posed for \(t\geq 0\) and for \(t\leq 0\) then \[ L= \sum_{i\leq m-r} a_{ij\alpha} \partial^ i_ t \partial^ j_ x \partial^ \alpha_ y\quad\text{with } a_{sr0}\neq 0. \]
Mathematics Subject Classification ID: 35E20
Mathematics Subject Classification ID: 35M99
zbMATH DE Number: 597449
zbMATH Keywords: \(C^ \infty\)-Goursat problem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195168662
OpenAlex ID: W2292833921
DOI: 10.2977/PRIMS/1195168662
description: scientific article; zbMATH DE number 597449