局部单调系数SPDE最优控制的存在性
Existence of optimal controls for SPDE with locally monotone coefficients
摘要：
研究了由局部单调系数的随机偏微分方程（SPDE）描述的系统在不同外力控制下的最优控制的存在性，这些外力控制是反馈控制.为了达到我们的目的，我们采用了H. Lisei，（Existence of optimal and non-最优控制for the stochastic Navier -斯托克斯方程，Nonlinear Analysis，51，（2002）95-118），其中研究了随机Navier-斯托克斯方程的最优控制的存在性。本文所得结果可应用于证明各种类型受控SPDE最优控制的存在性，如：随机非局部方程和局部单调的随机半线性方程;我们也将结果应用于单调方程，如随机反应扩散方程和随机线性方程.
英文摘要：
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are feedback controls. To attain our objective we adapt the argument of H. Lisei, (Existence of optimal and epsilon-optimal controls for the stochastic Navier - Stokes equation, Nonlinear Analysis, 51, (2002) 95-118) where the existence of optimal control to the stochastic Navier-Stokes equation was studied. The results obtained in the present paper may be applied to demonstrate the existence of optimal control to various types of controlled SPDEs such as: a stochastic nonlocal equation and stochastic semilinear equations which are locally monotone equations; we also apply the result to a monotone equation such as the stochastic reaction diffusion equation and to a stochastic linear equation.
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