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

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.