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Asymptotic behavior of solutions of complex discrete evolution equations: The discrete Ginzburg-Landau equation

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  • 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.
    Mathematics Subject Classification: Primary: 37L60, 34D45; Secondary: 35Q55.

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