Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation
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. Some of the theoretical results are tested by numerical simulations.
Keywords: Discrete Ginzburg-Landau
equation, lattice differential equations, blow-up in finite time, global attractors.
Received: May 2006; Revised: July 2007; Available Online: September 2007.
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