论文标题
具有退化和非分类非局部阻尼的一类可扩展光束的动力学
Dynamics of a class of extensible beams with degenerate and non-degenerate nonlocal damping
论文作者
论文摘要
这项工作涉及一类与可扩展光束相关的双曲进化方程的长期动力学的新结果，并具有三个明显的非局部非线性阻尼项。在第一个可能的堕落情况下，结果具有一个紧凑的全球吸引子家族的存在，以及对其Kolmogorov的$ \ Varepsilon $ -Entropy的厚度估算。然后，在非分类环境中，有用的非本地阻尼的结构导致存在有限维的紧凑型全局和指数吸引子。最后，在一个堕落和关键的框架中，证明存在有限的封闭全球吸引子但不紧凑的存在。为了证明证明，我们通过精致的估计值提供了几种新的技术结果，这些估计可以为非线性衰减问题的新分支开辟观点。
This work is concerned with new results on long-time dynamics of a class of hyperbolic evolution equations related to extensible beams with three distinguished nonlocal nonlinear damping terms. In the first possibly degenerate case, the results feature the existence of a family of compact global attractors and a thickness estimate for their Kolmogorov's $\varepsilon$-entropy. Then, in the non-degenerate context, the structure of the helpful nonlocal damping leads to the existence of finite-dimensional compact global and exponential attractors. Lastly, in a degenerate and critical framework, it is proved the existence of a bounded closed global attractor but not compact. To the proofs, we provide several new technical results by means of refined estimates that open up perspectives for a new branch of nonlinearly damped problems.
