Monotonicity method applied to the complex Ginzburg-Landau and related equations
type: Item
instance of: scholarly article
title: Monotonicity method applied to the complex Ginzburg-Landau and related equations
zbMATH Open document ID: 0995.35029
author: Noboru Okazawa
author: Tomomi Yokota
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-10-17T00:00:00Z
reviewed by: X. Xiang
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1733406
zbMATH Keywords: \(m\)-accretive operator
zbMATH Keywords: sectorial estimates
zbMATH Keywords: global existence of unique strong solutions
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7770
OpenAlex ID: W2054840050
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DOI: 10.1006/JMAA.2001.7770
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review text: A new inequality in monotonicity methods is derived. It is based on the sectorial estimates of \(-\Delta\) in \(L^{p+1}\) and the nonlinear operator \(u\mapsto|u|^{p-1}u\) appearing in the equation.NEWLINENEWLINENEWLINEBy the inequality the global existence of unique strong solutions is established for the complex Ginzburg-Landau equation. The inequality also yields the global existence of unique strong solution for nonlinear Schrödinger type equation with monotone nonlinearity.
description: scientific article; zbMATH DE number 1733406