Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
type: Item
instance of: scholarly article
title: Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
zbMATH Open document ID: 0829.35121
author: H. Nawa
published in: Journal of the Mathematical Society of Japan
publication date: 1996-01-15T00:00:00Z
review text: The nonlinear Schrödinger equation \[ 2i {\partial u \over \partial t} + \Delta u + |u |^{p - 1} u = 0, \quad (t,x) \in\mathbb{R}_+ \times\mathbb{R}^N \tag{1} \] arises in various domains of physics. The number \(p = 1 + 4/N\) is the critical number for the existence of blow-up solutions of (1). This article deals with this critical case. A singular solution of (1) is studied.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 758147
zbMATH Keywords: critical number
zbMATH Keywords: blow-up solutions
zbMATH Keywords: singular solution
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04640557
OpenAlex ID: W2083470323
DOI: 10.2969/JMSJ/04640557
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description: scientific article; zbMATH DE number 758147