随机泛函偏微分方程解的存在唯一性  

Existence and Uniqueness for Solution of Stochastic Functional Partial Differential Equations

作　　者：余国胜[1] YU Guosheng(School of Mathematics and Computer Science,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学数学与计算机科学学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2020年第3期24-30,共7页Journal of Jianghan University：Natural Science Edition

摘　　要：采用一种新的方法研究了可分Hilbert空间上随机泛函偏微分方程解的存在唯一性。首先由Burkholder-Davis-Gundy不等式和Gronwall引理证明了解的唯一性。然后通过构造新的迭代过程,得到迭代过程收敛于一个过程u(t)。最后证明u(t)恰好是随机泛函偏微分方程的解。In this paper,we made use of a new method to study the existence and uniqueness for solution of stochastic functional partial differential equations in separable Hilbert spaces.Firstly,by means of Burkholder-Davis-Gundy inequality and Gronwall lemma,the uniqueness of solution was obtained.Then,the iterative process converging to the process u(t)was obtained.Finally,we proved the convergent process u(t)was the solution of stochastic functional partial differential equations.

关 键 词：随机偏微分方程 能量解 存在唯一性 

分 类 号：O211.6[理学—概率论与数理统计]