Optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations |
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Authors: | Huaiqiang Yu Bin Liu |
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Institution: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, PR China |
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Abstract: | 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. |
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