Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation
Classical Analysis and ODEs
2007-05-23 v1 Dynamical Systems
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
Cite
@article{arxiv.math/0503297,
title = {Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation},
author = {Nikos I. Karachalios and Hector E. Nistazakis and Athanasios N. Yannacopoulos},
journal= {arXiv preprint arXiv:math/0503297},
year = {2007}
}