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Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
(2010-12-31)
The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence ...
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 ...
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 ...
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 ...
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 ...
Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation [Solutions localisées et mécanismes de filtrage pour les approximations de Galerkin discontinues de l'équation des ondes.]
(2010-12-31)
We perform a complete Fourier analysis of the semi-discrete 1-d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits ...
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 ...