On necessary conditions for the Cauchy problem for evolution equations to be well posed in the class \(C^ \infty\)
type: Item
instance of: scholarly article
title: On necessary conditions for the Cauchy problem for evolution equations to be well posed in the class \(C^ \infty\)
zbMATH Open document ID: 0854.35024
author: Keiichiro Kitagawa
published in: Journal of Mathematics of Kyoto University
publication date: 1993-05-16T00:00:00Z
review text: The author studies the Cauchy problem for equations of the form \[ Lu(t, x)= \Biggl[ t^k \partial^m_t- \sum^m_{j= 1} a_j(t, x_j \partial_x) \partial^{m- j}_t\Biggr] u(t, x)= 0,\;(t, x)\in [\tau, T]\times \Omega, \] with \(C^\infty\)-coefficients. He gives necessary conditions for this problem to have a unique solution.
Mathematics Subject Classification ID: 35G25
zbMATH DE Number: 169028
zbMATH Keywords: microlocal energy
zbMATH Keywords: well-posedness
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519489
OpenAlex ID: W2135947013
DOI: 10.1215/KJM/1250519489
description: scientific article; zbMATH DE number 169028