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.

参考文献 18

[1]	Grimmer R. Resolvent operator for integral equations in a Banach space. Tran Amer Math Soc, 1982, 273(1): 333-349 doi: 10.1090/S0002-9947-1982-0664046-4
[2]	Grimmer R, Kappel F. Series expansions of Volterra integrodifferential equations in Banach space. SIAM J Math Anal, 1984, 15(3): 595-604 doi: 10.1137/0515045
[3]	Grimmer R, Pritchhard A J. Analytic resolvent operators for integral equations in a Banach space. J Differ Equations, 1983, 50(2): 234-259 doi: 10.1016/0022-0396(83)90076-1
[4]	Dos Santos J, Henriquez H, Hernandez E. Existence results for neutral integro-differential equations with unbounded delay. J Integral Equ Appl, 2011, 23(2): 289-330
[5]	Zhu J, Fu X. Existence and regularity of solutions for neutral partial functional integro-differential equations with nonlocal conditions. J Fixed Point Theory Appl, 2020, 22(2): 1-25 doi: 10.1007/s11784-019-0746-3
[6]	Fu X, Huang R. Existence of solutions for neutral integro-differential equations with state-dependent delay. Appl Math Comput, 2013, 224: 743-759 doi: 10.1016/j.cam.2008.06.006
[7]	Hernandez E, $\rm{O}^{'}$Regan D. On a new class of abstract neutral integro-differential equations and applications. Acta Appl Math, 2017, 149: 125-137 doi: 10.1007/s10440-016-0090-1
[8]	Mokkedem F, Fu X. Approximate controllability of semi-linear neutral integro-differential systems with finite delay. Appl Math Comput, 2014, 242: 202-215
[9]	Ezzinbi K, Ghnimi S. Existence and regularity of solutions for neutral partial functional integrodifferential equations. Nonlinear Anal, 2010, 11(4): 2335-2344
[10]	Prato G D, Kwapien S, Zabczyk J. Regularity of solutions of linear stochastic equations in Hilbert spaces. Stochastics, 1988, 23(1): 1-23 doi: 10.1080/17442508708833480
[11]	Prevot C I. Existence, uniqueness and regularity w.r.t. the initial condition of mild solutions of SPDEs driven by Poisson noise. Infin Dimens Anal QU, 2010, 13(1): 133-163
[12]	Fu X. Existence and stability of solutions for nonautonomous stochastic functional evolution equations. J Inequal Appl, 2009, 1: 1-27
[13]	Prato G D, Zabczyk J. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press, 1992
[14]	Liu K. Stability of Infinite Dimensional Stochastic Differential Equations with Applications. London: Chapman Hall, 2006
[15]	Dieye M, Diop M A, Ezzinbi K. On exponential stability of mild solutions for some stochatic partial integrodifferential equations. Stat Probabil Lett, 2017, 123: 61-76 doi: 10.1016/j.spl.2016.10.031
[16]	Diop M A, Caraballo T. Asymptotic stability of neutral stochastic functional integro-differential equations. Electron Commun Prob, 2015, 20: 1-13
[17]	Huang H, Fu X. Asymptotic properties of solutions for impulsive neutral stochastic functional integro-differential equations. J Math Phys, 2021, 62(1): 013301 doi: 10.1063/1.5139964
[18]	Chaudhary R, Pandey D N. Existence and approximation of solution to stochatic fractional integro-differential equation with impulsive effects. Collect Math, 2018, 69(78): 181-204 doi: 10.1007/s13348-017-0199-1