文献类型：期刊文献

中文题名：N维空间中一类强阻尼非线性波动方程的解及其性质

英文题名：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]

第一作者：廖扬

机构：[1]河南财经政法大学数学与信息科学学院

第一机构：河南财经政法大学数学与信息科学学院

年份：2016

卷号：31

期号：6

起止页码：95-99

中文期刊名：轻工学报

外文期刊名：Journal of Light Industry

收录：CSTPCD

基金：河南省基础与前沿技术研究计划项目(132300410338)

语种：中文

中文关键词：N维空间;强阻尼;波动方程;整体吸引子;正则化

外文关键词：N-demensional space; strongly damped; wave equation; global attractors; regularity;

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.