Optimal control for two-dimensional stochastic second grade fluids |
| |
Authors: | Nikolai Chemetov Fernanda Cipriano |
| |
Institution: | 1. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Portugal;2. Centro de Matemática e Aplicações (CMA) FCT/UNL, Portugal;3. Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Portugal |
| |
Abstract: | This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition. |
| |
Keywords: | 35R60 49K20 60G15 60H15 76D55 Stochastic second grade fluids Backward stochastic partial differential equations Stochastic optimal control Necessary optimality condition |
本文献已被 ScienceDirect 等数据库收录! |