具扰动阻尼项波动方程的整体吸引子  

Global Attractors for a Class of Perturbed Damped Wave Equations

作　　者：张媛媛[1] 王宏伟[2] 

机构地区：[1]开封大学数学教研部,河南开封475000 [2]安阳师范学院数学与统计学院,河南安阳455000

出　　处：《重庆师范大学学报（自然科学版）》2015年第2期68-71,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.10971199);河南省教育厅科学技术研究重点项目(No.13B110137);2014年开封市工业科技攻关计划项目(No.1401012)

摘　　要：具扰动阻尼项波动方程在非线性发展方程、无穷维动力系统及数学物理方程中有一定的代表性,定义了一个连续半群,进而通过算子半群的方法,利用发展方程和无穷维动力系统的紧密关系,借助偏微分方程的一些标准技巧研究一类具扰动阻尼项波动方程的初边值问题,利用Soblev空间中重要不等式对非线性项进行估计,得到该类方程整体解的存在唯一性,且当空间维数N≤5时,在相对比较弱的条件下证明了上述问题整体吸引子的存在性,所得结果都是新的,并且扩展了文献原有的结果。The class of perturbed damped wave equation has certain representation in infinite-dimensional dynamical systems and mathematical physics equations. A continuous semigroup is defined. And through the method of semigroup,by the close relation- ship between evolution equations and infinite-dimensional dynamical systems,and using some standard methods, the initial boundary value problem for a class of perturbed damped wave equation is studied. By important inequality in Soblev Space, the non-linear terms are estimated. The existence and uniqueness of the global solutions for this class of equation are obtained. And when the space dimension N≤5,under rather mild conditions the dynamical system associated with the above-mentioned problem possesses a global attractor. The results are new and expand the literature originally results.

关 键 词：扰动阻尼项 整体解 整体吸引子 

分 类 号：O175.29[理学—数学]