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Journal of Mathematical Fluid Mechanics

, Volume 16, Issue 2, pp 211–223 | Cite as

Complex Ginzburg–Landau Equation with Absorption: Existence, Uniqueness and Localization Properties

  • Stanislav Antontsev
  • João-Paulo Dias
  • Mário Figueira
Article
  • 157 Downloads

Abstract

In this paper we study the time-dependent complex Ginzburg–Landau equation with a nonlinear absorbing term in \({\Omega \times(0,T),\, \Omega }\) open bounded set in \({\mathbb{R}^{n}}\) . We prove global existence and uniqueness of solutions for the initial and boundary-value problem and study the properties of localization and extinction of solutions in some special cases.

Mathematics Subject Classification (2010)

35 K15 35 B40 35Q35 

Keywords

Ginzburg–Landau equation absorption localization extinction 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Stanislav Antontsev
    • 1
  • João-Paulo Dias
    • 1
  • Mário Figueira
    • 1
  1. 1.CMAF/ULLisboaPortugal

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