Local well-posedness of the complex Ginzburg–Landau equation in bounded domains

Takanori Kuroda, Mitsuharu Otani

Research output: Contribution to journalArticle

Abstract

In this paper, we are concerned with the local well-posedness of the initial–boundary value problem for complex Ginzburg–Landau (CGL) equations in bounded domains. There are many studies for the case where the real part of its nonlinear term plays as dissipation. This dissipative case is intensively studied and it is shown that (CGL) admits a global solution when parameters appearing in (CGL) belong to the so-called CGL-region. This paper deals with the non-dissipative case. We regard (CGL) as a parabolic equation perturbed by monotone and non-monotone perturbations and follows the basic strategy developed in Ôtani (1982) to show the local well-posedness of (CGL) and the existence of small global solutions provided that the nonlinearity is the Sobolev subcritical.

LanguageEnglish
Pages877-894
Number of pages18
JournalNonlinear Analysis: Real World Applications
Volume45
DOIs
Publication statusPublished - 2019 Feb 1

Fingerprint

Complex Ginzburg-Landau Equation
Local Well-posedness
Ginzburg-Landau
Boundary value problems
Bounded Domain
Global Solution
Initial-boundary-value Problem
Parabolic Equation
Dissipation
Monotone
Well-posedness
Nonlinearity
Perturbation
Term

Keywords

  • Complex Ginzburg–Landau equation
  • Initial–boundary value problem
  • Local well-posedness
  • Subdifferential operator

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Local well-posedness of the complex Ginzburg–Landau equation in bounded domains. / Kuroda, Takanori; Otani, Mitsuharu.

In: Nonlinear Analysis: Real World Applications, Vol. 45, 01.02.2019, p. 877-894.

Research output: Contribution to journalArticle

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