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Existence of optimal controls for SPDE with locally monotone coefficients

The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotones coefficients controlled by different external forces which are feedback controls. We apply our result to various types of SPDEs such as stochastic 2-D Navier-Stokes equation, stochastic nonlocal equation, stochastic linear equations and stochastic semilinear equations. 

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