Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps
type: Item
instance of: scholarly article
title: Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps
zbMATH Open document ID: 1016.35023
DOI: 10.1007/BF02898235
author: Huaiyu Jian
author: Youde Wang
published in: Science in China. Series A
publication date: 2002-08-15T00:00:00Z
review text: The authors deal with the following boundary value problem for \(V_\varepsilon= (V^1_\varepsilon,\dots, V^m_\varepsilon):\Omega\to \mathbb{R}^m\), \[ \begin{cases} -\text{div}(A(x)\nabla V)= {B(x)V\over \varepsilon^2} (1-|V|^2)+ P(x)V\quad &\text{in }\Omega,\\ V(x)= g(x)\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(\Omega\subset \mathbb{R}^m\) is a smooth, bounded and simply connected domain. They prove that, under some suitable assumptions, all the vortices of (1) are pinned together to the minimum points of \(A(x)\) in \(\Omega\) as \(\varepsilon\to 0\). Moreover, the authors construct a self-similar solution in the evolution of harmonic maps. To this end they use so-called Pokhozhaev identity.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1782005
zbMATH Keywords: vortices
zbMATH Keywords: harmonic map
zbMATH Keywords: self-similar solutions
zbMATH Keywords: Pokhozhaev identity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02898235
OpenAlex ID: W1522421860
description: scientific article; zbMATH DE number 1782005