Displaying similar documents to “Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)”

Quasiconvex relaxation of multidimensional control problems with integrands (, , )

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands (, , ) in presence of a convex control restriction. The relaxed problem, wherein the integrand has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

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...

Spreadability, Vulnerability and Protector Control

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

Strong stabilization of controlled vibrating systems

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 ytt + A 0 y + u (t) B 0 y (t) = 0, t ∈ [0, +∞[, where A ...

Strong stabilization of controlled vibrating systems

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 = ⟨, ...

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

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...

Lower semicontinuity and relaxation results in BV for integral functionals with BV integrands

Micol Amar, Virginia De Cicco, Nicola Fusco (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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New -lower semicontinuity and relaxation results for integral functionals defined in BV() are proved, under a very weak dependence of the integrand with respect to the spatial variable . More precisely, only the lower semicontinuity in the sense of the -capacity is assumed in order to obtain the lower semicontinuity of the functional. This condition is satisfied, for instance, by the lower approximate limit of the integrand, if it is BV with respect to . Under this further...

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem         inf{ () +  () + (1 −  − ) () | Ω open in ℝ, || ≤ 1}, for  ∈ [0, 1],  +  ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

On the distribution of characteristic parameters of words

Arturo Carpi, Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

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For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...