Displaying similar documents to “On the Fattorini criterion for approximate controllability and stabilizability of parabolic systems”

Uniform local null control of the Leray-α model

Fágner D. Araruna, Enrique Fernández-Cara, Diego A. Souza (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with the distributed and boundary controllability of the so called Leray- model. This is a regularized variant of the Navier−Stokes system ( is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray- equations are locally null controllable, with controls bounded independently of . We also prove that, if the initial data are sufficiently small, the controls converge as → 0 to a null control of the Navier−Stokes equations....

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 ...

Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls

Alexander Khapalov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the one dimensional semilinear reaction-diffusion equation, governed in Ω = (0,1) by controls, supported on any subinterval of , which are the functions of time only. Using an asymptotic approach that we have previously introduced in [9], we show that such a system is approximately controllable at any time in both (0,1)( and [0,1], provided the nonlinear term grows at infinity no faster than certain power of . The latter depends on...

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...