论文标题
具有非翻译 - 紧凑外力的耗散PDE的均匀吸引者的熵估计值
Entropy estimates for uniform attractors of dissipative PDEs with non translation-compact external forces
论文作者
论文摘要
我们研究了Kolmogorov的非自主耗散PDE的统一吸引子的熵。主要关注外部力量不是翻译 - 压缩的情况。我们提出了一种新的一般方案，该方案使我们能够通过其船体的适当投影到翻译 - 紧凑型功能的空间来为各种外部力量提供此熵的上限。该结果概括了Vishik和Chepyzhov的众所周知的估计值。获得的结果应用于三个模型问题：具有差异式边界条件的亚质量3D抑制波方程，具有周期性边界条件的Quintic 3D波方程和有界域中的2D Navier-Stokes系统。还给出了某些非翻译 - 压缩的特殊外部力量的有限维均匀吸引子的例子。
We study the Kolmogorov's entropy of uniform attractors for non-autonomous dissipative PDEs. The main attention is payed to the case where the external forces are not translation-compact. We present a new general scheme which allows us to give the upper bounds of this entropy for various classes of external forces through the entropy of proper projections of their hulls to the space of translation-compact functions. This result generalizes well known estimates of Vishik and Chepyzhov for the translation-compact case. The obtained results are applied to three model problems: sub-quintic 3D damped wave equation with Dirichlet boundary conditions, quintic 3D wave equation with periodic boundary conditions and 2D Navier-Stokes system in a bounded domain. The examples of finite-dimensional uniform attractors for some special external forces which are not translation-compact are also given.
