Hamilton算子矩阵的半群生成定理

Generation Theorems of Semigroups for Hamiltonian Operator Matrices

研究了Hamilton算子矩阵的半群生成问题,得到其生成C_0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.

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 C_0 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.