Hille-Yosida定理在一类无穷维Hamiltion系统中的应用  

The Application of Hille-Yosida Theorem to a Class of Infinite Dimensional Hamiltonian System

作　　者：额布日力吐[1] 阿拉坦仓[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学的实践与认识》2012年第11期198-204,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10962004);高等学校博士学科点专项科研基金(20111501110001)

摘　　要：应用Hille-Yosida定理研究了无穷维Hamilton算子,得到了一个无穷维Hamilton系统初值问题解的存在性定理,并把结果应用在由一类双曲型偏微分方程导出的无穷维Hamilton系统中,给出了此类无穷维Hamilton系统解的存在性定理.Applying Hille-Yosida theorem, the infinite dimensional hamiltonian operators is investigated. Then it is proved that the existence theorem of solutions for a class of initial value problems of infinite dimensional hamiltonian systems. In particular, the obtained result is applied to the infinite dimensional hamiltonian system generated by a kind of hyperbolic partial differential equations and its the existence theorem of solutions is obtained.

关 键 词：无穷维Hamiltion系统 无穷维Hamiltion算子 算子半群 双曲型偏微分方程 

分 类 号：O177.1[理学—数学] O241.82[理学—基础数学]