A bifurcation analysis for the Ginzburg-Landau equation
type: Item
instance of: scholarly article
title: A bifurcation analysis for the Ginzburg-Landau equation
zbMATH Open document ID: 0943.35085
author: Myriam Comte
author: Petru Mironescu
published in: Archive for Rational Mechanics and Analysis
publication date: 2000-09-06T00:00:00Z
review text: The authors consider the following boundary-value problem for the Ginzburg-Landau equation \[ \begin{aligned}-\Delta u={1\over\varepsilon^2} u_\varepsilon(1-|u_\varepsilon|^2)\quad &\text{in }B,\\ u_\varepsilon(z)= z^d\quad &\text{on }\partial B,\end{aligned}\tag{1} \] where \(B\) is the unit ball of \(\mathbb{R}^2\), \(d\in\mathbb{N}^*\) and \(\varepsilon>0\) is a parameter. They establish that for \(d=2\), there exists a bifurcation branch, defined for \(\varepsilon< \varepsilon_2\), \(\varepsilon\) near to \(\varepsilon_2\), emanating from the radial solutions to (1) at \(\varepsilon= \varepsilon_2\). In a neighborhood of \(\varepsilon_2\), the solution on the bifurcation branch admit exactly two zeroes.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1239962
zbMATH Keywords: boundary-value problem
zbMATH Keywords: Ginzburg-Landau equation
zbMATH Keywords: bifurcation
reviewed by: Stefan Balint
MaRDI profile type: Publication
full work available at URL: s002050050119
OpenAlex ID: W2078890770
DOI: 10.1007/S002050050119
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description: scientific article; zbMATH DE number 1239962