广义分布半群与退化发展方程的分布解

葛照强

数学学报 ›› 2018, Vol. 61 ›› Issue (1) : 79-88.

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数学学报 ›› 2018, Vol. 61 ›› Issue (1) : 79-88. DOI: 10.12386/A2018sxxb0008
论文

广义分布半群与退化发展方程的分布解

    葛照强
作者信息 +

Generalized Distribution Semi-groups and Distributional Solution of Degenerate Evolution Equations

    Zhao Qiang GE
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文章历史 +

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.

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.

关键词

广义分布半群 / 分布解 / 退化发展方程

Key words

generalized distribution semi-group / distributional solution / degenerate evolution equation

引用本文

导出引用
葛照强. 广义分布半群与退化发展方程的分布解. 数学学报, 2018, 61(1): 79-88 https://doi.org/10.12386/A2018sxxb0008
Zhao Qiang GE. Generalized Distribution Semi-groups and Distributional Solution of Degenerate Evolution Equations. Acta Mathematica Sinica, Chinese Series, 2018, 61(1): 79-88 https://doi.org/10.12386/A2018sxxb0008

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基金

国家自然科学基金资助项目(61174081)

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