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Now showing items 1-10 of 15

#### 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 ...

#### 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 ...

#### 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.]

(Comptes Rendus Mathematique, 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 ...