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This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…

Optimization and Control · Mathematics 2016-10-11 Maoning Tang , Qingxin Meng

We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid)…

Optimization and Control · Mathematics 2009-03-09 Francesca Bucci , Irena Lasiecka

We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…

Probability · Mathematics 2025-11-26 Stefano Bonaccorsi , Adrian Zalinescu

We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…

Analysis of PDEs · Mathematics 2024-10-21 Xinyue Evelyn Zhao , Yixiang Wu , Rachel Leander , Wandi Ding , Suzanne Lenhart

This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…

Optimization and Control · Mathematics 2018-02-27 Romuald Elie , Ludovic Moreau , Dylan Possamaï

This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…

Optimization and Control · Mathematics 2018-04-30 Christian Clason , Armin Rund , Karl Kunisch

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…

Optimization and Control · Mathematics 2019-06-11 Xiuchun Bi , Jingrui Sun , Jie Xiong

In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than…

Optimization and Control · Mathematics 2019-07-10 Shailin Ji , Haodong Liu

Inverse Stefan problem arising in modeling of laser ablation of biomedical tissues is analyzed, where information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the…

Analysis of PDEs · Mathematics 2017-10-25 Ugur G. Abdulla , Jonathan Goldfarb

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…

Optimization and Control · Mathematics 2016-06-14 Anil Kumar , Amiya K. Pani , Mohan C. Joshi

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

Analysis of PDEs · Mathematics 2018-10-26 Harbir Antil , Ken Shirakawa , Noriaki Yamazaki

The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…

Optimization and Control · Mathematics 2021-01-27 Qi Lü , Xu Zhang

We consider parabolic equations on bounded smooth open sets $\Om\subset \R^N$ ($N\ge 1$) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator $\mathscr{L} \coloneqq - \Delta + (-\Delta)^{s}$…

Analysis of PDEs · Mathematics 2022-02-28 Jean-Daniel Djida , Gisele Mophou , Mahamadi Warma

In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…

Optimization and Control · Mathematics 2023-03-06 Kareem T. Elgindy

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…

Optimization and Control · Mathematics 2018-09-05 Peter Benner , Christoph Trautwein

We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In the case of multiplicative noise, existence of optimal controls and necessary conditions for optimality are derived. In…

Optimization and Control · Mathematics 2021-10-28 Wilhelm Stannat , Lukas Wessels

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…

Probability · Mathematics 2015-05-13 S. Bonaccorsi , F. Confortola , E. Mastrogiacomo

We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…

Probability · Mathematics 2019-01-23 Erhan Bayraktar , Jinniao Qiu

In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a source/control placement outside the domain where the PDE is…

Optimization and Control · Mathematics 2019-04-16 Harbir Antil , Deepanshu Verma , Mahamadi Warma