{"title":"EXISTENCE AND NON-EXISTENCE OF GLOBAL SOLUTIONS FOR THE SEMILINEAR COMPLEX GINZBURG-LANDAU TYPE EQUATION IN HOMOGENEOUS AND ISOTROPIC SPACETIME","authors":"Makoto Nakamura, Y. Sato","doi":"10.2206/kyushujm.75.169","DOIUrl":null,"url":null,"abstract":"The Cauchy problem for the semilinear complex Ginzburg–Landau type equation is considered in homogeneous and isotropic spacetime. Global solutions and their asymptotic behaviours for small initial data are obtained. The non-existence of non-trivial global solutions is also shown. The effects of spatial expansion and contraction are studied through the problem.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/kyushujm.75.169","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The Cauchy problem for the semilinear complex Ginzburg–Landau type equation is considered in homogeneous and isotropic spacetime. Global solutions and their asymptotic behaviours for small initial data are obtained. The non-existence of non-trivial global solutions is also shown. The effects of spatial expansion and contraction are studied through the problem.
期刊介绍：
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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