{"title":"Ginzburg–Landau equation with fractional Laplacian on a upper- right quarter plane","authors":"J F Carreño-Diaz and E I Kaikina","doi":"10.1088/1361-6544/ad4adf","DOIUrl":null,"url":null,"abstract":"We consider the initial-boundary value problem for the Ginzburg–Landau equation with fractional Laplacian on a upper-right quarter plane where , and is a fractional Laplacian defined as We study the main questions of the theory of IBV- problems for nonlocal equations: the existence and uniqueness of a solution, the asymptotic behavior of the solution for large time and the influence of initial and boundary data on the basic properties of the solution. We generalize the concept of the well-posedness of IBV- problem in the based Sobolev spaces to the case of a multidimensional domain. We also give optimal relations between the orders of the Sobolev spaces to which the initial and boundary data belong. The lower order compatibility conditions between initial and boundary data are also discussed.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"22 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinearity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1088/1361-6544/ad4adf","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the initial-boundary value problem for the Ginzburg–Landau equation with fractional Laplacian on a upper-right quarter plane where , and is a fractional Laplacian defined as We study the main questions of the theory of IBV- problems for nonlocal equations: the existence and uniqueness of a solution, the asymptotic behavior of the solution for large time and the influence of initial and boundary data on the basic properties of the solution. We generalize the concept of the well-posedness of IBV- problem in the based Sobolev spaces to the case of a multidimensional domain. We also give optimal relations between the orders of the Sobolev spaces to which the initial and boundary data belong. The lower order compatibility conditions between initial and boundary data are also discussed.
期刊介绍：
Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest.
Subject coverage:
The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal.
Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena.
Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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