具强阻尼项波动方程整体吸引子的Hausdorff维数

摘要

The behavior of the global attractors for a class of strongly damped wave equations was studied. By some standard methods the nonlinear term was estimated. By embedding theorem and the method of semigroup, it was obtained that under rather mild conditions the attractors of the above-mentioned problem had Hausdorff dimensions.%研究了一类具强阻尼项的波动方程整体吸引子的性质.借助偏微分方程的一些标准技巧对非线性项进行估计,利用嵌入定理和算子半群的方法证明了在相对比较弱的条件下上述问题的整体吸引子具有Hausdorff维数.