摘要
本文讨论了一类在弦和梁的微小振动中出现的二次算子族L（λ）=λ2M-iλK-A的谱分布问题，进而将所得结论与无穷维Hamilton算子联系起来，利用无穷维Hamilton算子的特殊结构，得到了一类非负无穷维Hamilton算子的谱分布，这为无穷维Hamilton算子的半群方法提供了理论保证．
In this paper, we discuss the spectrum of a class quadratic operator pencils which appears in vibrations of strings and beams. Meanwhile, we gained the spectrumof the infinite-dimensional Hamiltonian operators making use of these conclusions to the infinite-dimensional Hamiltonian operators and considering the special structure of infinite-dimensional Hamiltonian operators. This provides us with theoretical guarantee to discuss the method of semi-group to the infinite-dimensional Hamiltonian operators.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2012年第4期665-672,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10962004)
关键词
无穷维HAMILTON算子
二次算子族
谱
infinite-dimensional Hamiltonian operators
quadratic operator pencils
spectrum
