A. Bernoussi (2010)
Mathematical Modelling of Natural Phenomena
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In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: , and . These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution
Tiziana Durante, Taras A. Mel’nyk (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...
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
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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.
Bernard Bonnard, Jean-Baptiste Caillau, Gabriel Janin (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is = d + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the...
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with feedback stabilization of second order equations of
the form
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper deals with feedback stabilization of second order equations of the form + + = 0, ∈ [0, +∞[, where is a densely defined positive selfadjoint linear operator on a real Hilbert space with compact inverse and is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control = ⟨, ...
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 ...