Existence of optimal controls for stochastic partial differential equations with fully local monotone coefficients
Abstract
This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled stochastic partial differential equations with fully monotone coefficients by a minimizing sequence for the control problem. Using the Faedo-Galerkin approximations, the uniform estimates and the tightness in some appropriate space for the Faedo-Galerkin approximating solution can be obtain to prove the well-posedness of the controlled stochastic partial differential equations with fully monotone coefficients. The results obtained in the present paper may be applied to various types of controlled stochastic partial differential equations, such as the controlled stochastic convection diffusion equation.
Cite
@article{arxiv.2501.02027,
title = {Existence of optimal controls for stochastic partial differential equations with fully local monotone coefficients},
author = {Gaofeng Zong},
journal= {arXiv preprint arXiv:2501.02027},
year = {2025}
}
Comments
34 pages. arXiv admin note: substantial text overlap with arXiv:2209.06657 by other authors