Related papers: A boundary control problem for the pure Cahn-Hilli…
In this paper, we consider an optimal bilinear control problem for the nonlinear Schr\"{o}dinger equations with singular potentials. We show well-posedness of the problem and existence of an optimal control. In addition, the first order…
In this paper, we study a boundary control problem associated to the stationary Rayleigh-B\'enard-Marangoni (RBM) system in presence of controls for the velocity and the temperature on parts of the boundary. We analyze the existence,…
We consider a heat conduction problem $S$ with mixed boundary conditions in a $n$-dimensional domain $\Omega$ with regular boundary and a family of problems $S_{\alpha}$ with also mixed boundary conditions in $\Omega$, where $\alpha>0$ is…
In this paper, we study the necessary and sufficient conditions for ensuring the well-posedness of the stochastic singular systems. Moreover, we investigate the stochastic singular linear-quadratic control problems, considering both finite…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
The paper arXiv:1804.11290 contains well-posedness and regularity results for a system of evolutionary operator equations having the structure of a Cahn-Hilliard system. The operators appearing in the system equations were fractional…
In this paper we deal with a doubly nonlinear Cahn-Hilliard system, where both an internal constraint on the time derivative of the concentration and a potential for the concentration are introduced. The definition of the chemical potential…
In this paper, we continue the study of some controllability issues for the forward stochastic heat equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
We consider optimal control problems governed by systems describing the unsteady flows of an incompressible second grade fluid with Navier-slip boundary conditions. We prove the existence of an optimal solution and derive the corresponding…
In this manuscript, we consider a control system governed by a general ordinary differential equation on a Riemannian manifold, with its endpoints satisfying some inequalities and equalities, and its control constrained to a closed convex…
This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…
We discuss a class of linear control problems in a Hilbert space setting. This class encompasses such diverse systems as port-Hamiltonian systems, Maxwell's equations with boundary control or the acoustic equations with boundary control and…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
This paper investigates the necessary optimality conditions for uniformly overtaking optimal control on infinite horizon in the free end case. %with free right endpoint. In the papers of S.M.Aseev, A.V.Kryazhimskii, V.M.Veliov, K.O.Besov…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
This paper is intended to tackle the control problem associated with an extended phase field system of Cahn-Hilliard type that is related to a tumor growth model. This system has been investigated in previous contributions from the…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…