摘要
利用经典的算子半群理论,研究了一类强阻尼具有热效应的耦合杆方程的初边值问题,证明了该系统解的存在唯一性和连续性,引入一个算子半群;利用经典的算子半群分解方法,验证了该半群分解后,一部分指数衰减,另一部分紧的;再由解对初值的连续依赖性,吸收集的不变性等,证明了该系统存在整体吸引子.
By using the classic theory of operator semigroup,the initial boundary value problem for a class of coupled elastic rod equation with strong damping and thermal effect was investigated.The existence and uniqueness of the solution were proved and a operator semigroup was introduced.According to the solution＇s continuity depending on the initial value,and the invariance of absorbing set,the existence of the global attractor for the mentioned system was proved by decomposing operator semigroup classically,with one part of the decomposed semigroup decaying exponentially and the other being compact.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2012年第1期28-31,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)
山西省青年科技研究基金资助项目(2011021002-2)
关键词
非线性
热源项
扇形算子
整体吸引子
nonlinearity
heat source term
sectorial operator
global attractor
