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Numerical approximation of null controls for the heat equation : Ill-posedness and remedies
(Inverse Problems, 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 ...
Stationary waves to viscous heat-conductive gases in half-space: Existence, stability and convergence rate
(Mathematical Models and Methods in Applied Sciences, 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 ...
A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
(Multiscale Modeling and Simulation, 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
(Journal of Systems Science and Complexity, 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 ...
A systematic method for building smooth controls for smooth data
(Discrete and Continuous Dynamical Systems - Series B, 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 ...
The Hardy inequality and the heat equation in twisted tubes
(Journal des Mathematiques Pures et Appliquees, 2010-12-31)
We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for ...
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
(Milan Journal of Mathematics, 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
(SIAM Journal on Mathematical Analysis, 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 ...
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
(Archive for Rational Mechanics and Analysis, 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 ...
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]
(Comptes Rendus Mathematique, 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 ...