Related papers: A boundary control problem for the pure Cahn-Hilli…
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain…
In this work, we address some optimal control problems related to the evolution of two isothermal, incompressible, immisible fluids in a two dimensional bounded domain. A distributed optimal control problem is formulated as the minimization…
The initial boundary value problem for a Cahn-Hilliard system subject to a dynamic boundary condition of Allen-Cahn type is treated. The vanishing of the surface diffusion on the dynamic boundary condition is the point of emphasis. By the…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
We consider numerical approximations and error analysis for the Cahn-Hilliard equation with reaction rate dependent dynamic boundary conditions (P. Knopf et. al., arXiv, 2020). Based on the stabilized linearly implicit approach, a…
In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…
The existence problem for {C}ahn--{H}illiard system with dynamic boundary conditions and time periodic conditions is discussed. We apply the abstract theory of evolution equations by using viscosity approach and the Schauder fixed point…
The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…
We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…
In this article, we are concerned about the velocity tracking optimal control problem for 3D critical convective Brinkman-Forchheimer equations defined on a simply connected bounded domain $\mathbb{D}\subset\mathbb{R}^3$ with…
This paper is concerned with an optimal control problem governed by nonsmooth semilinear elliptic partial differential equations with both distributed and boundary unilateral pointwise control constraints, in which the nonlinear coefficient…
In this paper, we consider a two-dimensional diffuse interface model for the phase separation of an incompressible and isothermal binary fluid mixture with matched densities. This model consists of the Navier--Stokes equations, nonlinearly…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
This paper is devoted to prove the exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We consider the case where the coupling matrix A…
The Allen-Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint which may involve either the solution inside…