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2005, 2005(Special): 476-486. doi: 10.3934/proc.2005.2005.476

Remarks on the asymptotic behavior of solutions of complex discrete Ginzburg-Landau equations

N. I. Karachalios 1, , H. E. Nistazakis 2, and  A. N. Yannacopoulos 3,

1. 

Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece
2. 

Department of Telecommunications Science and Technology, University of the Peloponesse, Tripolis 22100, Greece
3. 

Department of Statistics and Actuarial Science, University of the Aegean, Karlovassi 83200, Samos, Greece

Received  September 2004 Revised  March 2005 Published  September 2005

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. The theoretical estimates, are tested by numerical simulations.
Keywords: Discrete Ginzburg-Landau equation, lattice dynamical systems, global attractors., blowup in finite time.
Mathematics Subject Classification: Primary: 37L60, 34D45; Secondary: 35Q5.
Citation: N. I. Karachalios, H. E. Nistazakis, A. N. Yannacopoulos. Remarks on the asymptotic behavior of solutions of complex discrete Ginzburg-Landau equations. Conference Publications, 2005, 2005 (Special) : 476-486. doi: 10.3934/proc.2005.2005.476
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