| 一类无穷维Hamilton算子的半群生成定理 |
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| 引用本文： | 阿拉坦仓,黄俊杰.一类无穷维Hamilton算子的半群生成定理[J].高校应用数学学报(A辑),2006,21(3):357-364. |
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| 作者姓名： | 阿拉坦仓 黄俊杰 |
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| 作者单位： | 内蒙古大学,数学系,内蒙古,呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金(10162003)，内蒙古自然科学基金(200508010103)，内蒙古大学高层次引进人才科研启动基金 |
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| 摘 要： | 研究了无穷维H am ilton算子生成C0半群的问题,得到了类无穷维H am ilton算子生成C0半群的一个充分条件.把结果应用在一类双曲型混合问题生成的无穷维H am ilton算子上,证明此类算子生成C0半群,并利用H ille-Y osida定理进一步说明了结果的正确性和有效性.另外,还给出了波动方程相应的无穷维H am ilton算子所生成的C0半群的具体表达式.
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| 关 键 词： | 无穷维Hamilton算子 C0半群 无穷小生成元 |
| 文章编号： | 1000-4424（2006）03-0357-08 |
| 收稿时间： | 2004-08-19 |
| 修稿时间： | 2004年8月19日 |
A theorem on C0 semigroups generated by a class of infinite dimensional Hamiltonian operators |
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| Alatancang,HUANG Jun-jie.A theorem on C0 semigroups generated by a class of infinite dimensional Hamiltonian operators[J].Applied Mathematics A Journal of Chinese Universities,2006,21(3):357-364. |
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| Authors: | Alatancang HUANG Jun-jie |
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| Institution: | Department of Mathematics, Neimongol University, Hohhot 010021 ,China |
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| Abstract: | The problem in which the infinite dimensional Hamiltonian operators generate semigroups is investigated,and a sufficient condition of generating semigroups is obtained for a class of infinite dimensional Hamiltonian operators.The results are applied to the infinite dimensional Hamiltonian operators generated by a class of mixed problems of hyperbolic PDE's,and it is showed that these operators generate semigroups.The correctness and effectiveness of the results are further demonstrated by Hille-Yosida's theorem.Besides,the expression of semigroup generated by an infinite dimensional Hamiltonian operator corresponding to a wave equation is given. |
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| Keywords: | infinite dimensional Hamiltonian operator C_0 semigroup infinitesimal generator |
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