N维空间中一类强阻尼非线性波动方程的解及其性质  

A class of strongly damped nonlinear wave equation solution of N-demensional space and its properties

作　　者：廖扬[1] 周晓宇[1] 

机构地区：[1]河南财经政法大学数学与信息科学学院

出　　处：《轻工学报》2016年第6期95-99,共5页Journal of Light Industry

基　　金：河南省基础与前沿技术研究计划项目(132300410338)

摘　　要：将强阻尼非线性波动方程在三维空间解的性质由三维推广到N(N>3)维,利用标准的Galerkin方法和Sobolev嵌入定理研究了弱解在该空间下的存在性,运用内积做出了解的耗散估计,并采用Gronwall引理证明了整体吸引子的存在性.The properties of three dimensional space solution of strongly damped nonlinear wave equation by 3D was expanded to N dimensional space（ N 3）. A standard Galerkin method and the Sobolev embedding theorem were utilized to study the existence of weak solution under the space. The inner product was used to make the solution＇s dissipation estimates,and the Gronwall lemma was used to prove the existence of the attractor.

关 键 词：N维空间 强阻尼 波动方程 整体吸引子 正则化 

分 类 号：O176.3[理学—数学] O177.91[理学—基础数学]