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Controllability of Schrödinger equations

Karine Beauchard (2005/2006)

Séminaire Équations aux dérivées partielles

One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite time, by...

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.

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