The time-periodic solution to a 2D generalized Ginzburg-Landau equation
type: Item
instance of: scholarly article
title: The time-periodic solution to a 2D generalized Ginzburg-Landau equation
zbMATH Open document ID: 1005.35011
author: Rong Yuan
author: Boling Guo
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-07-04T00:00:00Z
review text: This paper is devoted to study the 2D generalized Ginzburg-Landau equation \[ u_t=\rho u+(1+i\nu) \Delta u-(1+i\mu) |u|^{2\sigma} \cdot u+\alpha \lambda_1\cdot \nabla\bigl( |u|^2\cdot u\bigr)+ \beta( \lambda_2 \cdot\nabla u)|u|^2+f,\tag{1} \] where \(\Omega=[0,L] \times [0,L]\), \(\rho,\sigma,L\) are positive numbers, \(\alpha,\beta, \nu,\mu\) are real numbers, and \(\lambda_1,\lambda_2\) are real vectors. Assuming that the function \(f\) is \(\omega\)-periodic in time and \(u(x+T,t)= u(x,t)\), the authors prove both existence and uniqueness of the time periodic solution of (1). To this end, they use both the Galerkin method and Leray-Schauder fixed point arguments.
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1763702
zbMATH Keywords: Leray-Schauder fixed point arguments
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jmaa.2001.7737
OpenAlex ID: W2043761668
cites work: Length scales in solutions of the complex Ginzburg-Landau equation
cites work: Finite dimensional behaviour for the derivative Ginzburg-Landau equation in two spatial dimensions
cites work: Weak and strong solutions of the complex Ginzburg-Landau equation
cites work: Q5890172
DOI: 10.1006/JMAA.2001.7737
description: scientific article; zbMATH DE number 1763702