Numerical computations for motion of vortices governed by a hyperbolic Ginzburg-Landau system
type: Item
instance of: scholarly article
title: Numerical computations for motion of vortices governed by a hyperbolic Ginzburg-Landau system
zbMATH Open document ID: 1153.35361
DOI: 10.1016/S0362-546X(01)00812-4
author: Takeyuki Nagasawa
author: Kazuaki Nakane
author: Seiro Omata
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-09-17T00:00:00Z
review text: This paper deals with the problem \(u_{tt}-\Delta u = (2/\delta)(1-| u| ^ 2)u\) on a Lipschitz domain of \(\mathbb R^M\) with values in \(\mathbb R^N\), where \(\delta\) is a positive constant. Numerical computations on a square (\(M=N=2\), \(\delta=0.1\)) are presented, illustrating bouncing vortices (if Dirichlet conditions are imposed), and reflection of vortices at the boundary (in the case of Neumann conditions). Some results for \(M=N=3\) are also reported. The method consists in solving a semi-discretized, implicit scheme by a variational method. Some estimates on semi-discretized problems, as \(\Delta t\to 0\), are given.
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 58E50
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1801695
MaRDI profile type: Publication
cites work: Ginzburg-Landau vortices
cites work: Stable solutions with zeros to the Ginzburg-Landau equation with Neumann boundary condition
cites work: Stability of nonconstant steady-state solutions to a Ginzburg–Landau equation in higher space dimensions
cites work: Ginzburg-landau equation and stable steady state solutions in a non-trivial domain
cites work: Q3704862
cites work: Q3973988
cites work: Q4203187
cites work: Numerical analysis for the discrete Morse semiflow related to the Ginzburg–Landau functional
cites work: On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables
cites work: Q4321143
full work available at URL: s0362-546x(01)00812-4
OpenAlex ID: W2014122156
description: scientific article; zbMATH DE number 1801695