Related papers: Neumann boundary optimal control problems governed…
We consider the equation $-\epsilon^{2}\Delta u + u = u^ {p}$ in a bounded domain $\Omega\subset\R^{3}$ with edges. We impose Neumann boundary conditions, assuming $1<p<5$, and prove concentration of solutions at suitable points of…
We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration…
In this paper, we consider the exact boundary controllability and the exact boundary synchronization (by groups) for a coupled system of wave equations with coupled Robin boundary controls. Owing to the difficulty coming from the lack of…
We present a waveform relaxation version of the Dirichlet-Neumann and Neumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain…
The goal of this paper is to address some optimal control and shape optimisation problems arising from bulk-surface cooperative systems. The basic model under consideration is the following: letting $\Omega$ be a fixed domain, we assume…
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…
In this paper we study the existence, the optimal regularity of solutions, and the regularity of the free boundary near the so-called \emph{regular points} in a thin obstacle problem that arises as the local extension of the obstacle…
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…
This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…
We investigate the control problem of harmonic map heat flow by means of an external magnetic field. In contrast to the situation of a parabolic system with internal or boundary control, the magnetic field acts as the coefficients of the…
In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain $\Omega \subset \mathbb{R}^N$ with the inhomogeneous Neumann boundary condition. We emphasize that the domain can be non-convex in…
Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in…
We study the parabolic free boundary problem of obstacle type $$ \lap u-\frac{\partial u}{\partial t}= f\chi_{{u\ne 0}}. $$ Under the condition that $f=Hv$ for some function $v$ with bounded second order spatial derivatives and bounded…
This paper studies the lower bound for the blow-up time $T^{*}$ of the heat equation $u_t=\Delta u$ in a bounded convex domain $\Omega$ in $\mathbb{R}^{N}(N\geq 2)$ with positive initial data $u_{0}$ and a local nonlinear Neumann boundary…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
We prove well posedness and stability in $\mathbf{L}^1$ for a class of mixed hyperbolic-parabolic non linear and non local equations in a bounded domain with no flow along the boundary. While the treatment of boundary conditions for the…