具有强阻尼的非线性梁方程的全局吸引子  

Global Attractor for the Nonlinear Beam Equations with Strongly Damping Term

作　　者：任永华[1] 张建文[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2014年第1期7-10,共4页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11172194);山西省自然科学基金资助项目(2010011008);太原理工大学校基金资助项目(900103-03020715)

摘　　要：研究了齐次Dirichlet边界条件下非线性强阻尼梁方程的长时间动力学行为.以经典的算子半群理论和能量的估计技巧为依据,获得了能量的一致衰退估计;通过相空间中新范数的引入,得到了系统的整体解所对应的解半群存在一致有界吸收集;利用半群分解技术,证明了具有强阻尼项的非线性梁方程解的全局吸引子在空间E上的存在性.Abstract： The long-time dynamical behavior of the nonlinear beam equations with strongly damping term is discussed under the homogeneous Dirichlet boundary conditions. Firstly, based on the classical semigroup the- orem and energy estimates, the energy uniformly decay estimate is obtained. Then, the uniformly bounded absorbing set for the associated semigroup which corresponds to the global solution of system is obtained by in- troducing a new norm in phase space. Lastly, using the suitable decomposition of the semigroup, the exist- ence of global attractors for the nonlinear beam equations with strongly damping term in the space E is prov-

关 键 词：非线性梁方程 强阻尼 全局吸引子 等价模 

分 类 号：O175[理学—数学]