带调和势的非线性Shrdinger方程整体吸引子的维数估计(英文)

An Estimate of the Dimensions of the Global Attractor for the Nonlinear Schrdinger Equation with Harmonic Potential

研究了带调和势的非线性Shrdinger方程:iut+uxx-x2u+｜u｜2u+iαu=f(x),α>0的长时间动力学行为,给出了该方程整体吸引子的Hausdorff维数和Fractal维数的上界估计.

In this paper, the long time behavior of solution for the nonlinear Schr6dinger equation with harmonic potential ：iut＋uxx-x^2u＋｜u｜^2＋iau=f（x）,a〉0 is studied. The estimates of the upper bounds of Hausdorff and Fractal dimensions for the global attractors are obtained.