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Displaying similar documents to “A singular controllability problem with vanishing viscosity”

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters and Δ. We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order ...

Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control

Larissa V. Fardigola (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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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.

Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control

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.

Controllability problems for the 1-D wave equation on a half-axis with the Dirichlet boundary control

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.

Controllability of a simplified model of fluid-structure interaction

S. Ervedoza, M. Vanninathan (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially symmetric case, this system can be controlled...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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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 ...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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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 ...

Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons

Mikhail Belishev, Aleksandr Glasman (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

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

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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...