| 广义分布半群与退化发展方程的分布解 |
| |
| 引用本文： | 葛照强.广义分布半群与退化发展方程的分布解[J].数学学报,2018,61(1):79-88. |
| |
| 作者姓名： | 葛照强 |
| |
| 作者单位： | 西安交通大学应用数学系 西安 710049 |
| |
| 基金项目： | 国家自然科学基金资助项目（61174081） |
| |
| 摘 要： | 在Banach空间中引进了由有界线性算子引导的广义分布半群的新概念,并讨论了它的有关性质.在我们的方法中,广义分布半群的生成元可以不是稠定的.此外,还引进了退化发展方程在Laplace变换意义下的分布解,应用广义分布半群给出了退化发展方程分布解的构造性表达式.
|
| 关 键 词： | 广义分布半群 分布解 退化发展方程 |
Generalized Distribution Semi-groups and Distributional Solution of Degenerate Evolution Equations |
| |
| Zhao Qiang GE.Generalized Distribution Semi-groups and Distributional Solution of Degenerate Evolution Equations[J].Acta Mathematica Sinica,2018,61(1):79-88. |
| |
| Authors: | Zhao Qiang GE |
| |
| Institution: | Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
| |
| Abstract: | We introduce a new concept of generalized distribution semi-groups induced by a bounded linear operator in Banach space and discuss the properties of this concept. In our approach, the generator of a generalized distribution semi-group may not be densely defined. Also introduced is the distributional solution of degenerate evolution equation in the sense of Laplace transformation. The constructive expression of the distributional solution for the degenerate evolution equation is given by the generalized distribution semi-group. |
| |
| Keywords: | generalized distribution semi-group distributional solution degenerate evolution equation |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
