Now showing items 1-10 of 15
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
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
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]
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 ...
Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
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 ...
A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
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 ...
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
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
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]
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.]
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 ...
Optimal control and vanishing viscosity for the burgers equation
[No abstract available]