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Journal of Evolution Equations

, Volume 14, Issue 2, pp 403–415 | Cite as

Finite-time blowup for a complex Ginzburg–Landau equation with linear driving

  • Thierry Cazenave
  • João-Paulo Dias
  • Mário Figueira
Article

Abstract

In this paper, we consider the complex Ginzburg–Landau equation \({u_t = e^{i\theta} [\Delta u + |u|^\alpha u] + \gamma u}\) on \({\mathbb{R}^N}\), where \({\alpha > 0,\,\gamma \in \mathbb{R}}\) and \({-\pi /2 < \theta < \pi /2}\). By convexity arguments, we prove that, under certain conditions on \({\alpha,\theta,\gamma}\), a class of solutions with negative initial energy blows up in finite time.

Mathematics Subject Classification (2010)

35Q56 35B44 

Keywords

Complex Ginzburg–Landau equation damping finite-time blowup energy variance 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Thierry Cazenave
    • 1
  • João-Paulo Dias
    • 2
  • Mário Figueira
    • 2
  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie Curie and CNRSParis Cedex 05France
  2. 2.Centro de Matemática e Aplicações FundamentaisUniversidade de LisboaLisbonPortugal

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