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Controllability of Schrödinger equation with a nonlocal term

Mariano De Leo, Constanza Sánchez Fernández de la Vega, Diego Rial (2014)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and...

Controllability of semilinear stochastic integrodifferential systems

Krishnan Balachandran, S. Karthikeyan, Jeong-Hoon Kim (2007)

Kybernetika

In this paper we study the approximate and complete controllability of stochastic integrodifferential system in finite dimensional spaces. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Picard iteration technique.

Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Hugo Leiva (2015)

Nonautonomous Dynamical Systems

In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this...

Controllability of three-dimensional Navier–Stokes equations and applications

Armen Shirikyan (2005/2006)

Séminaire Équations aux dérivées partielles

We formulate two results on controllability properties of the 3D Navier–Stokes (NS) system. They concern the approximate controllability and exact controllability in finite-dimensional projections of the problem in question. As a consequence, we obtain the existence of a strong solution of the Cauchy problem for the 3D NS system with an arbitrary initial function and a large class of right-hand sides. We also discuss some qualitative properties of admissible weak solutions for randomly forced NS...

Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Mouffak Benchohra, Lech Górniewicz, Sotiris K. Ntouyas (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.

Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti, Jean-Claude Vivalda (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...

Controllability theorem for nonlinear dynamical systems

Michał Kisielewicz (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.

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