相关论文: Neumann boundary optimal control problems governed…

We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost…

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…

We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…

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…

In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type govern the evolution of coupled diffuse phase transition…

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the…

We consider semilinear parabolic optimal control problems subject to Neumann boundary conditions, control constraints, and an infinite time horizon. The control constraints are pointwise in time, but they can be pointwise or integral in the…

We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…

A boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved. Key words: Cahn-Hilliard equation,…

First, let $u_{g}$ be the unique solution of an elliptic variational inequality with source term $g$. We establish, in the general case, the error estimate between $u_{3}(\mu)=\mu u_{g_{1}}+ (1-\mu)u_{g_{2}}$ %(the convex combination of two…

We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…

This paper analyzes the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where an additive noise occurs in the Neumann boundary condition. The convergence is established for general filtrations, and…

In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat…

A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, treated as an unknown Neumann boundary condition. Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data Assimilation…

We study solutions to a variational equation that models heat control on the boundary. This problem can be thought of as the two phase parabolic Signorini problem. We show that when the solution has a sign on the boundary, the study of the…

We consider an optimal control problem with tracking-type cost functional constrained by the Cattaneo equation, which is a well-known model for delayed heat transfer. In particular, we are interested the asymptotic behaviour of the optimal…

This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…

We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…

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…

In this paper, we study the control of the linear heat equation with a space and time dependent coefficient function by the Dirichlet and Neumann boundary control laws. This equation models the heat diffusion and space, time dependent heat…