Related papers: On an evolutionary dynamical system of the first o…
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with…
In this paper we introduce a method to find the minimal control time for the null controllability of 1D first-order linear hyperbolic systems by one-sided boundary controls when the coefficients are regular enough.
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein…
In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding…
The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary.…
In recent years, controllability problems for dispersive systems have been extensively studied. This work is dedicated to proving a new type of controllability for a dispersive fifth order equation that models water waves, what we will now…
In this paper we consider a nonlinear system of PDEs coupling the viscous Cahn-Hilliard-Oono equation with dynamic boundary conditions enjoying a similar structure on the boundary. After proving well-posedness of the corresponding initial…
In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…
In this note, we consider an optimal control problem associated to a differential equation driven by a H\"{o}lder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend…
This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex.…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
These notes provide a survey of recent results and open problems on the boundary control of moving sets. Motivated by the control of an invasive biological species, we consider a class of optimization problems for a moving set $t\mapsto…
The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed…