一类耦合的非线性KdV方程组的Hausdorff维数和分形维数

Upper bound of dimensions of Hausdorff and fractal for a generalized coupled KdV system

研究了一类耦合的非线性KdV方程组解的渐进性质 ,根据非线性Galerkin方法和Leray Schauder定理 ,应用线性变分的方法 ,得到了Hausdorff维数dH(A)≤J0 和分形维数dF(A)≤ 1 +2bb/3caJ30 -bJ0的上界估计 .

By nonlinear Galerkin method and Leray Schauder theorem, the solution of asymptote property for the generalized couple KdV equation is investigated, and the estimates are made of the upper bounds of Hausdorff d H (A) and fractal dimensions d F (A) for the global attractors, where d H (A)≤J 0, d F (A)≤J 01+2bb/3caJ 3 0-bJ 0 .