数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 936-946.

• 论文 • 上一篇    下一篇

Hamilton算子矩阵的半群生成定理

刘杰1,2, 黄俊杰1, 阿拉坦仓1,3   

  1. 1 内蒙古大学数学科学学院 呼和浩特 010021;
    2 内蒙古大学满洲里学院 内蒙古满洲里 021400;
    3 呼和浩特民族学院数学系 呼和浩特 010051
  • 收稿日期:2014-02-27 修回日期:2015-04-21 出版日期:2015-10-25 发布日期:2015-10-25
  • 通讯作者: 黄俊杰,huangjunjie@imu.edu.cn E-mail:huangjunjie@imu.edu.cn
  • 基金资助:

    国家自然科学基金(11461049,11371185)和内蒙古自然科学基金(2013JQ01,2013ZD01)资助

Generation Theorems of Semigroups for Hamiltonian Operator Matrices

Liu Jie1,2, Huang Junjie1, Alatancang1,3   

  1. 1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021;
    2 Manzhouli College, Inner Mongolia University, Inner Mongolia Manzhouli 021400;
    3 Department of Mathematics, Huhhot University for Nationalities, Hohhot 010051
  • Received:2014-02-27 Revised:2015-04-21 Online:2015-10-25 Published:2015-10-25

摘要:

研究了Hamilton算子矩阵的半群生成问题,得到其生成C0半群的若干充分必要条件,并给出其成为半群无穷小生成元时的谱分布.作为应用,基于Hamilton系统的半群方法,给出一类四阶微分方程混合问题的古典解.

关键词: Hamilton算子矩阵, C0半群, 谱分布

Abstract:

This paper deals with the generation problem of semigroups for Hamiltonian operator matrices. Some necessary and sufficient conditions are obtained for Hamiltonian operator matrices to generate C0 semigroups. Then the spectral location of such operator matrices are further obtained. As applications, the solutions of mixed problems for a class of fourth-order partial differential equations are given, based on the semigroup method of Hamiltonian system.

Key words: Hamiltonian operator matrix, C0 semigroup, Spectral distribution

中图分类号: 

  • O175.3