| 上三角无穷维Hamilton算子半群生成定理 |
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| 引用本文： | 刘杰,阿拉坦仓.上三角无穷维Hamilton算子半群生成定理[J].内蒙古大学学报(自然科学版),2009,40(5). |
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| 作者姓名： | 刘杰 阿拉坦仓 |
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| 作者单位： | 内蒙古大学数学科学学院,呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金资助项目，内蒙古自然科学基金资助项目(200508010103)} |
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| 摘 要： | 研究了上三角无穷维Hamilton算子生成C0半群问题,得到了上三角无穷维Hamilton算子生成C0半群的一个充分条件.把结果应用在一类二阶常系数抛物型偏微分方程初值问题导出的无穷维Hamilton算子上,并证明此类算子生成C0半群,此外还给出了所生成C0半群的具体表达式,从而进一步说明了结果的正确性.
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| 关 键 词： | 无穷维Hamilton算子 C0半群 无穷小生成元 |
A Theorem on C0 Semigroups Generated by Upper-triangular-type Infinite Dimensional Hamiltonian Operators |
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| LIU Jie,Alatancang.A Theorem on C0 Semigroups Generated by Upper-triangular-type Infinite Dimensional Hamiltonian Operators[J].Acta Scientiarum Naturalium Universitatis Neimongol,2009,40(5). |
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| Authors: | LIU Jie Alatancang |
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| Abstract: | The problem that the upper-triangular-type infinite dimensional Hamiltonian operators generate semigroups is investigated,and a sufficient condition of generating semigroups is obtained. The results are applied to the upper-triangular-type infinite dimensional Hamiltonian operators generated by a class of initial valve problem of second order constant coefficient parabolic PDEs,and it is showed that these operators generate semigroups. Furthermore,the expression of a semigroup generated by this class of Hamiltonian operators is given. So, the correctness of the results are further demonstrated. |
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| Keywords: | infinite dimensional Hamiltonian operator C_0 semigroup {infinitesimal generator |
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