Larissa V. Fardigola (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper necessary and sufficient conditions of L-controllability and approximate L-controllability are obtained for the control system = − , (0) = (), > 0, ∈ (0), where ≥ 0, > 0, ∈ L(0) is a control. This system is considered in the Sobolev spaces.
Larissa V. Fardigola (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper necessary and sufficient conditions of L-controllability and approximate L-controllability are obtained for the control system = − , (0) = (), > 0, ∈ (0), where ≥ 0, > 0, ∈ L(0) is a control. This system is considered in the Sobolev spaces.
Larissa V. Fardigola (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper necessary and sufficient conditions of L-controllability and approximate L-controllability are obtained for the control system = − , (0) = (), > 0, ∈ (0), where ≥ 0, > 0, ∈ L(0) is a control. This system is considered in the Sobolev spaces.
Sorin Micu, Ionel Rovenţa (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This article considers the linear 1-d Schrödinger equation in (0) perturbed by a vanishing viscosity term depending on a small parameter > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that, for any time sufficiently large but independent of and for each initial datum in ...
Sorin Micu, Ionel Rovenţa (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This article considers the linear 1-d Schrödinger equation in (0) perturbed by a vanishing viscosity term depending on a small parameter > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that, for any time sufficiently large but independent of and for each initial datum in ...
Mariano De Leo, Constanza Sánchez Fernández de la Vega, Diego Rial (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, () = − +() +() , that arises in quantum semiconductor models. Here () is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and () 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...
Mikhail Belishev, Aleksandr Glasman (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ . Let Ω ⊂ Ω be the subdomain filled by waves at the moment , the moment at which the waves fill the whole of . The following effect occurs: for small enough the system is approximately controllable in Ω whereas for larger a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics...