Gevrey regularizing effect for the initial value problem for a dispersive operator
type: Item
instance of: scholarly article
title: Gevrey regularizing effect for the initial value problem for a dispersive operator
zbMATH Open document ID: 1072.35173
author: Kazuo Taniguchi
published in: Osaka Journal of Mathematics
publication date: 2005-03-18T00:00:00Z
review text: The Gevrey regularizing effect for equations of Schrödinger type has been studied by other authors. It is known that the initial value problem \[ \begin{cases} i\partial_tu+ \Delta^lu &= f(u),\\ u(0,x) &= u_0(x)\end{cases} \] has a solution \(u(t, x)\) which belongs to a Gevrey class of order \(\max(s/2l, 1)\) in \(t\neq 0\) if the initial data \(u_0(x)\) belongs to a Gevrey class of order \(s\). In this paper, the author studies the Gevrey regularizing effect of this initial value problem where \(\Delta^l\) is replaced by a semi-elliptic operator \(A\).
reviewed by: Anthony D. Osborne
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 2147092
zbMATH Keywords: Gevrey regularizing effect
zbMATH Keywords: dispersive operator
zbMATH Keywords: initial value problem
zbMATH Keywords: Schrödinger type equations
zbMATH Keywords: semi-elliptic operator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2147092