Optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Yu, Huaiqiang¹  Liu, Bin¹ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

关键词: Stochastic partial differential equations;    Boundary control;    Necessary conditions;    Convex state constraints;    BSPDE with non-homogeneous double boundary conditions;   

DOI  :  10.1016/j.jmaa.2012.05.071

来源: Elsevier

【 摘 要 】

We study the boundary control problems for stochastic parabolic equations with Neumann boundary conditions. Imposing super-parabolic conditions, we establish the existence and uniqueness of the solution of state and adjoint equations with non-homogeneous boundary conditions by the Galerkin approximations method. We also find that, in this case, the adjoint equation (BSPDE) has two boundary conditions (one is non-homogeneous, the other is homogeneous). By these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free