具有局部Kelvin Voigt型阻尼的波动方程的全局吸引子问题  

Global Attractor for the Semilinear Wave Equation with Localize d Kelvin-Voigt Damping

作　　者：李坤 LI Kun(School of Science,Henan Institute of Technology,Xinxiang,453003,China)

机构地区：[1]河南工学院理学部,河南新乡453003

出　　处：《河南工学院学报》2024年第5期36-40,共5页Journal of Henan Institute of Technology

摘　　要：局部KelvinV oigt阻尼的特点为仅在边界的一部分上存在有效结构性阻尼且该阻尼是无界的,这致使很难使用经典的无穷维动力系统理论来研究具有局部KelvinV oigt型阻尼的波动方程的长时间行为。文章基于一致稳定性估计通过验证解半群的拟稳定性质来证明有限维全局吸引子的存在性。The characters of localized Kelvin-Voigt damping in the theoretical analysis are that the effectively structural damping is located in a portion of the boundary and the structural damping term is unbounded,which prevent us from studying the long-time behavior by traditional theory of infinite dimensional dynamical systems.Based on the uniform stabilization estimates,we will establish the existence of a global attractor with finite fractal dimension by the quasi-stability property for the semilinear wave equation with localized Kelvin-Voigt damping.

关 键 词：全局吸引子 分形维数 拟稳定性 局部KelvinV oigt型阻尼 

分 类 号：O19[理学—数学]