带非齐次Dirichlet边界的随机非线性Schrodinger方程解的整体存在性

Global Existence of a Stochastic Nonlinear Schrodinger Equation with Inhomogeneous Dirichlet Boundary Value

研究带有非齐次Dirichlet边界条件且带有加性白噪声的随机非线性Schr?dinger方程在H^1(R^+)空间中的整体解存在性.在偏微分方程理论、泛函分析和随机分析等知识基础上,在质量泛函和能量泛函的基础上引入第三个"桥梁"泛函,通过It?公式建立3个泛函之间的关系,最终获得带非齐次Dirichlet边界的随机非线性Schr?dinger方程在具有竞争非线性的各种情况下解的有界性,从而获得方程的解的整体存在性.

We study the global existence of solutions in the energy space Hi （ ） for the stochastic nonlinear Schrfidinger equa- tion with Dirichlet boundary value. Based on the partial differential equations theories, functional analysis and stochastic analysis, we introduce the third bridge functional on the basis of quality functional and energy functional and establish the relationship among these three functionals by It6 formula. We get the boundedness of the solution of the the stochastic nonlinear SchrSdinger equation with inho- mogeneous Dirichlet boundary value, additive white noise and competitive nonlinear terms in each cases and finally obtain the global existence of solution of the equation.