Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
Probability
2010-03-18 v2 Analysis of PDEs
Optimization and Control
Abstract
We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrisable control sets.
Keywords
Cite
@article{arxiv.1001.3165,
title = {Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces},
author = {Zdzislaw Brzezniak and Rafael Serrano},
journal= {arXiv preprint arXiv:1001.3165},
year = {2010}
}