On the dimension of the attractor for the wave equation with nonlinear damping
On the dimension of the attractor for the wave equation with nonlinear damping
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DOI：
10.3934/cpaa.2005.4.165
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发表时间：
2004-12
影响因子：
1
通讯作者：
D. Pražák
中科院分区：
文献类型：
--
作者：
D. Pražák
给出了非线性阻尼波动方程整体吸引子的分维的一个显式估计。非线性是某些多项式增长的光滑函数。作为一个副产品，我们估计的时间$\tau$解决方案运营商的指数吸引子的尺寸，提供$\tau$是足够大的。证明中使用的主要工具是所谓的轨迹法。
We give an explicit estimate of the fractal dimension of the global attractor to the wave equation with nolinear damping. The nonlinearities are smooth functions of certain polynomial growth. As a by-product we estimate the dimension of the exponential attractor for the time $\tau$ solution operator provided that $\tau$ is sufficiently large. The main tool used in the proof is the so-called method of the trajectories.