Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation

Details Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation

2005-03-15

arxiv.org/abs/math/0503297v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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