Approximate controllability of nonlinear stochastic partial differential systems with infinite delay

Advances in Difference Equations

Guangyan Qing¹  Hanwen Ning² 

[1] Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan, P.R. China;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P.R. China

关键词: stochastic;    partial differential systems;    approximate controllability;    Banach contraction theorem;    infinite delay;   

DOI  :  10.1186/s13662-015-0434-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper aims to investigate approximate controllability of stochastic nonlinear partial differential systems with infinite delay. In the systems under study, nonlinearity and control variable exist both in drift and diffusion terms, and controllability problems are considered in the framework with a novel Banach space, which not only leads to some difficulties in deriving the properties of interest but also bring some opportunities to study the system in a more general framework. With the help of a new fundamental lemma established in this paper and some useful inequality techniques, some improved results for approximate controllability of stochastic partial differential systems are obtained by using the Banach contraction theorem without introducing any additional restraints on the terms of the system. An example of stochastic heat equation is also provided to illustrate our results.

【 授权许可】

CC BY