离散的Burgers-Ginzburg-Landau方程组的吸引子

文章通过对空间变量的有限差分方法离散了具有周期边值的Ｂｕｒｇｅｒｓ Ｇｉｎｚｂｕｒｇ Ｌａｎｄａｕ方程组．研究了这个离散方程组初值问题解的适定性．证明了当差分网格足够大时离散方程组存在吸引子，并得到了吸引子的Ｈａｕｓｄｏｒｆｆ维数和分形维数的上界估计．这个上界不会随着网格的加细而无限增大，因此数值分析离散的有限维系统的吸引子可以近似探讨原无限维系统的吸引子．

The Attractors of the discretized Burgers-Ginzburg-Landau Equations

In this paper, the Burgers Ginzburg Landau equations with periodic boundary condition are discretized by the finite difference method in spatial direction. It is proved that for each mesh size, there exists an attractor of the discretized system. The bounds for the Hausdorff and fractal dimensions of the attractors are obtained for sufficiently small mesh size. The bounds are independent of the mesh iszes, so that the discretized finite dimensional systems can be used to analyze, numerically and approximately, the infinite dimensional dynamical system of the Burgers Ginzburg Landau equations.