Remarks on the asymptotic behavior of solutions of complex discrete Ginzburg-Landau equations
N. I. Karachalios - Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece (email)
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. The theoretical estimates, are tested by numerical simulations.
Keywords: Discrete Ginzburg-Landau equation, lattice dynamical systems, blowup in finite time, global attractors.
Received: September 2004; Revised: March 2005; Published: September 2005.