复离散发展方程解的渐近性态：离散Ginzburg-Landau方程
Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation
摘要：
研究了复离散Ginzburg- Landau型发展方程的渐近性态.根据问题的非线性和数据，我们发现不同的动力学行为，从整体存在的解决方案和整体吸引子，在有限时间爆破。我们提供的爆破时间的估计，不仅取决于初始数据，但也对晶格的大小。通过数值模拟对部分理论结果进行了验证。
英文摘要：
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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