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2007, Volume 19, Issue 4: 711-736. Doi: 10.3934/dcds.2007.19.711
This issue Previous Article Existence of a semilinear elliptic system with exponential nonlinearities Next Article Metric Hopf-Lax formula with semicontinuous data

Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation

  • 1.

    Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos

  • 2.

    Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi GR 83200, Samos

  • 3.

    Department of Statistics, Athens University of Economics and Business, Patission 76 GR 10434, Athens

Received:  April 30, 2006
Revised:  June 30, 2007
Published:  September 2007
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    Abstract
  • We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions and global attractors to blow-up in finite time. We provide estimates for the blow-up time, depending not only on the initial data but also on the size of the lattice. Some of the theoretical results are tested by numerical simulations.
    Mathematics Subject Classification: Primary: 37L60, 34D45; Secondary: 35Q55.

    Citation:
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