研究一类具耗散项的四阶非线性波动方程初边值问题整体吸引子的分形维数问题,利用偏微分方程的一些标准技巧对非线性项进行估计,用L轨道法证明了在相对较弱的条件下上述问题的整体吸引子具有有限分形维数.
The initial boundary value problem and fractal dimensions of global attractors for a class of four order nonlinear wave equations with dissipation were studied. By some standard methods the non-linear term was estimated. By L-track, it was obtained that under rather mild conditions the attractors of the above-mentioned problem had finite fractal dimensions.