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Numerical approximation of null controls for the heat equation : Ill-posedness and remedies
(2010-12-31)
The numerical approximation of exact or trajectory controls for the wave equation is known to be a delicate issue, since the pioneering work of Glowinski-Lions in the nineties, because of the anomalous behavior of the ...
Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system
(2010-12-31)
This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ...
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
(2010-12-31)
A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers ...
Strichartz estimates for the Schrödinger equation on a tree and applications
(2010-12-31)
In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We obtain Strichartz-like estimates for the linear semigroup and apply them to ...
Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach
(2010-12-31)
In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space ...
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
(2010-12-31)
In this paper, we present and analyze a variational model in nonlinear elasticity that allows for cavitation and fracture. The main idea in unifying the theories of cavitation and fracture is to regard both cavities and ...
A systematic method for building smooth controls for smooth data
(2010-12-31)
We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z0 in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability ...
Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension [Minimiseurs de l'énergie explicits d'une barre incompressible, élastique, mais fragile, soumise à une extension uniaxiale]
(2010-12-31)
A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of ...
A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
(2010-12-31)
We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan-Vese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266-277], where the ...
Localized solutions for the finite difference semi-discretization of the wave equation [Solutions localisées pour la semi-discrétisation par différences finies de l'équation des ondes]
(2010-12-31)
We study the propagation properties of the solutions of the finite difference space semi-discrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that ...