Stability Of Solutions To Stochastic Partial Differential Equations With Delays

Stochastic partial differential equations with delays can be used to describe and study manynatural phenomena. However, in general it is not easy to solve the solution of stochastic delaypartial differential system. Therefore, researchers are more concerned about the qualitativeproperties of solutions for stochastic partial differential equations with delays, such as the existence,uniqueness and stability of solutions. So far, there are no results on the existence, uniqueness andstability of mild solutions to stochastic delay partial differential driven by Poisson jumps system, aswell as a class of impulsive stochastic partial differential equations with delays and Poisson jumps,as well as impulsive stochastic delay partial differential equations with Markovian jumps. Themain object of this paper is to solve above-mentioned problems.This paper has five chapters, specific arrangements as follows:Chapter1is the preface. Firstly, the methods used to study the stability of mild solutions tostochastic partial differential equations with delays are introduced as well as the purpose andsignificance of this paper. Secondly, the basic framework and content of this article are given.Finally, the necessary foundation knowledge in this paper is stated.In chapter2, we discuss the existence, uniqueness and p th moment exponential stability ofmild solutions of stochastic partial differential equations with delays and Poisson jumps. Based onBanach fixed point theory, we get the sufficient condition to ensure the obtained result in thischapter.In chapter3, we study the qualitative properties of mild solutions to impulsive stochasticdelay partial differential driven by Poisson jumps system. In the first place, by Banach fixed pointtheory, we solve the existence, uniqueness and p th moment exponential stability of the mildsolution for the system Considered in this chapter. Next, we prove the almost surely p th momentexponential stability of mild solutions by using Borel-Cantelli lemma and the related properties ofStochastic integral.In chapter4, By using Banach fixed point theory, we prove the p th moment asymptoticstability of mild solutions to impulsive stochastic partial differential equations with delays and Markovian jumps. In the process of proof, we obtain some sufficient conditions in order to ensurethe mild solution of the system considered in this chapter is p th moment asymptotically stable.Chapter5is a Summary. We summarize the main work and innovation in this paper,meanwhile, we point out the place of the improvement of this article in the future.