一类中立型随机发展方程解的存在性与正则性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 238-248.

一类中立型随机发展方程解的存在性与正则性

宋玉莹(),范虹霞^*()

兰州交通大学数理学院兰州 730070

收稿日期:2022-01-18 修回日期:2022-07-19 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*范虹霞, E-mail: ffls0217@126.com
作者简介:宋玉莹, E-mail: songyuying97@163.com
基金资助:
国家自然科学基金(11561040)

Existence and Regularity of Solutions for a Class of Neutral Stochastic Evolution Equations

Song Yuying(),Fan Hongxia^*()

College of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070

Received:2022-01-18 Revised:2022-07-19 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(11561040)

摘要/Abstract

摘要：

该文在 Hilbert 空间中研究一类中立型随机偏泛函积分微分方程解的存在性与正则性. 利用预解算子理论及不动点定理获得 Hilbert 空间 $X$ 及 $X_{\alpha}$ 上 mild 解的存在性结果, 且验证在某些条件下方程的 mild 解就是其古典解, 推广已有的相关结果.

关键词: 中立型随机积分微分方程, 正则性, mild 解, 预解算子理论, 不动点定理

Abstract:

In this paper, we study the existence and regularity of solutions for a class of neutral stochastic partial functional integro-differential equations in Hilbert space. By using resolvent operator theory and fixed point theorem, the existence results of mild solutions on Hilbert space $X$ and $X_{\alpha}$ are obtained. It is verified that the mild solution of the equation is its classical solution under some conditions, which generalizes the relevant results.

Key words: Neutral stochastic integro-differential equation, Regularity, Mild solution, Resolvent operator theory, Fixed point theorem

中图分类号:

O175.6

宋玉莹, 范虹霞. 一类中立型随机发展方程解的存在性与正则性[J]. 数学物理学报, 2023, 43(1): 238-248.

Song Yuying, Fan Hongxia. Existence and Regularity of Solutions for a Class of Neutral Stochastic Evolution Equations[J]. Acta mathematica scientia,Series A, 2023, 43(1): 238-248.

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