带无限延迟和泊松跳项的一类NSPDE温和解的存在唯一性  

The Existence and Uniqueness of Mild Solution for a Class of NSPDE with Infinite Delay and Poisson Jumps

作　　者：王治 杜先云 WANG Zhi;DU Xian-yun(Department of Basic Course, Officers College of CAPF, Chengdu 610213, China;School of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China)

机构地区：[1]武警警官学院基础部,四川成都610213 [2]成都信息工程大学应用数学学院,四川成都610225

出　　处：《数学的实践与认识》2018年第7期223-229,共7页Mathematics in Practice and Theory

摘　　要：在可分的实希尔伯特空间中考虑了一类带有无限延迟和泊松跳项的非自治随机偏微分方程温和解的性质问题．通过使用泛函分析中的巴拿赫不动点定理，主要证明了相应方程温和解的存在唯一性．与针对此非自治随机偏微分方程先前的研究工作相比，得出的结论是新的，并且文中使用的方法可以进一步推广到其他的非自治随机微分方程的研究中.In this paper,the problems properties of mild solutions for a class of non-autonomous stochastic partial differential equations with infinite delay and poisson jumps are considered in real separable Hilbert spaces.By using the Banach fixed point theorem,the existence and uniqueness of mild solution is studied. Compared with the previous work, our results is new for this non-autonomous stochastic partial differential equations and this method can generalize to others equations.

关 键 词：存在唯一性 非自治随机偏微分方程 无限延迟 泊松跳 

分 类 号：O211.63[理学—概率论与数理统计]