摘要
利用算子半群理论研究一类杆上热扩散方程初边值问题的周期解.把热扩散方程化为抽象Banach空间中的发展方程,利用上下解单调迭代方法得到抽象发展方程mild解的存在唯一性.把抽象结果应用于热扩散方程,得到热扩散方程初边值问题mildω-周期解的存在性与唯一性.
To discuss the period solutions of initial-boundary value problems for the heat diffusion equations.Firstly,the theory of operators semigroup are used when the heat diffusion equation are turned into the evolution equations in the abstract banach spaces;secondly,the existence and uniqueness results of mild solution to the abstract evolution equation are obtained through the monotone iterative method;finally the gained abstract results are applied to the heat diffusion equations.The existence and uniqueness results of mild period solution are obtained for initial-boundary value problems to the heat diffusion equations.
出处
《内蒙古师范大学学报（自然科学汉文版）》
CAS
北大核心
2016年第4期449-452,456,共5页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目(11371031)
陕西省自然科学基础研究计划资助项目(2014JM1027)
陕西省教育厅专项科研计划项目(2013JK0572)
宝鸡文理学院重点科研计划项目(ZK16028
ZK16113)
关键词
热扩散方程
MILD解
初边值问题
正C0-半群
周期解
the heat diffusion equations
mild solution
initial-boundary value problem
positive C0-semigroup
period solutions
