Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的存在唯一性  

Existence and Uniqueness of Mild Solution to Neutral Stochastic Partial Functional Differential Equations with Infinite Delay in Hilbert Spaces

作　　者：余国胜 YU Guosheng(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学人工智能学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2021年第5期18-23,共6页Journal of Jianghan University：Natural Science Edition

摘　　要：首先给出了Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的定义,然后利用解析半群的性质,Burkholder-Davis-Gundy不等式和Banach不动点定理证明了该Hilbert空间上无穷时滞中立型随机偏泛函微分方程适度解的存在唯一性,最后举出一个实例说明了所得结果的有效性。Firstly,the definition of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces was introduced.Then,by means of the properties of analytic semigroups,Burkholder-Davis-Gundy inequality,and Banach fixed point theorem,the existence and uniqueness of the mild solution to neutral stochastic partial functional differential equations with infinite delay in Hilbert spaces were obtained.Finally,an example was given to illustrate the results.

关 键 词：无穷时滞 中立型随机偏泛函微分方程 适度解 存在唯一性 

分 类 号：O211.6[理学—概率论与数理统计]