The Ginzburg--Landau equation: Posed in a quarter-plane
type: Item
instance of: scholarly article
title: The Ginzburg--Landau equation: Posed in a quarter-plane
zbMATH Open document ID: 0777.35060
author: Charles Bu
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
review text: Several existence and uniqueness theorems are stated for the Ginzburg- Landau (GL) equation. First, one extends the global existence theorem for the Cauchy problem of the GL equation on a bounded domain to a theorem on an unbounded domain by using a semigroup technique. In the case of the GL equation in a quarter-plane, one proves a local existence-uniqueness theorem for the classical solution and gives a criterion of small initial-boundary data. Finally, it is shown that, for some special values of the parameters, this local solution is also a global solution.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35A07
zbMATH DE Number: 399081
zbMATH Keywords: Ginzburg-Landau equation
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: unbounded domain
zbMATH Keywords: small initial-boundary data
zbMATH Keywords: local solution
reviewed by: Guy Jumarie
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1228
OpenAlex ID: W2018977426
DOI: 10.1006/JMAA.1993.1228
description: scientific article; zbMATH DE number 399081