摘要
首先，对于主算子是ｍ次积分半群的无穷小生成元的一类发展方程引入了温和解的概念，并讨论了温和解与古典解的关系．其次，讨论了ｍ次积分半群的指数稳定性，并给出了两个充要条件．
G Fei, XIANG Xiao-ling (Department of mathematics, Guizhou Education College, Guiyang Guizhou, 550003, China Department of mathematics, Guizhou University, Guiyang Guizhou 550025, China) Abstract: In this paper, we introduce the mild solution for a class of evolution equations whose principle operator is the infinitesimal generator of a m-times integrated semigroup and discuss the relation between mild solutions and classical solutions. The exponential stability of rn-times integrated semigroups is inverstigated and two sufficient and necessary conditions are obtained.
出处
《应用泛函分析学报》
CSCD
2001年第4期359-365,共7页
Acta Analysis Functionalis Applicata
关键词
m次积分半群
无穷小生成元
指数稳定性
温和解
m-times integrated semigroup
infinitesimal generator
exponential stability
mild solution
