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.
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
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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 ...
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 ...
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...
Fábio Júlio Valentim (2012)
Annales de l'I.H.P. Probabilités et statistiques
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Fix a polynomial of the form () = + ∑2≤≤ =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑ ...
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...