Displaying similar documents to “On the null-controllability of diffusion equations”

On the null-controllability of diffusion equations

Gérald Tenenbaum, Marius Tucsnak (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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This work studies the null-controllability of a class of abstract parabolic equations. The main contribution in the general case consists in giving a short proof of an abstract version of a sufficient condition for null-controllability which has been proposed by Lebeau and Robbiano. We do not assume that the control operator is admissible. Moreover, we give estimates of the control cost. In the special case of the heat equation in rectangular domains, we provide an alternative...

Remarks on non controllability of the heat equation with memory

Sergio Guerrero, Oleg Yurievich Imanuvilov (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support

Luis Alberto Fernández, Alexander Yuri Khapalov (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.

Null controllability of nonlinear convective heat equations

Sebastian Aniţa, Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in .

Some new results related to the null controllability of the 1 - d heat equation

Antonio López, Enrique Zuazua (1997-1998)

Séminaire Équations aux dérivées partielles

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We address three null controllability problems related to the 1 - d heat equation. First we show that the 1 - d heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation...