Browsing Former Research Lines by Title
Now showing items 93112 of 220

Hardtype inequalities for $\Delta_{\lambda}$Laplacians
(20151231)We derive Hardytype inequalities for a large class of subelliptic operators that belong to the class of (Formula presented.) Laplacians and find explicit values for the constants involved. Our results generalize previous ... 
Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials
(20091231)We address the question of exact controllability of the wave and Schrodinger equa\tions perturbed by a singular inversesquare potential. Exact boundary controllability is proved in the range of subcritical coefficients ... 
Hardy inequality and Pohozaev identity for operators with boundary singularities: Some applications
(20111231)We consider the Schrödinger operator Aλ:=δλ/x2, λ∈R, when the singularity is located on the boundary of a smooth domain Ω⊂RN, N≥1.The aim of this Note is two folded. Firstly, we justify the extension of the classical ... 
Hardy type inequalities for $\Delta_{\lambda}$Laplacians
(20160101)We derive Hardytype inequalities for a large class of subelliptic operators that belong to the class of $\Delta_{\lambda}$Laplacians and find explicit values for the constants involved. Our results generalize previous ... 
High frequency wave packets for the Schrödinger equation and its numerical approximations [Paquets d'ondes à haute fréquence pour l'équation de Schrödinger et ses approximations numériques]
(20111231)We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semidiscretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in ... 
Homogenization of fiber reinforced brittle materials: The extremal cases
(20091231)We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: ... 
Homogenization of the Neumann problem in perforated domains: An alternative approach
(20111231)The main result of this paper is a compactness theorem for families of functions in the space SBV (Special functions of Bounded Variation) defined on periodically perforated domains. Given an open and bounded set Ω n, and ... 
Identification of the class of initial data for the insensitizing control of the heat equation
(20091231)This paper is devoted to analyze the class of initial data that can be insensitized for the heat equation. This issue has been extensively addressed in the literature both in the case of complete and approximate insensitization ... 
Incompressible limit of the nonisentropic NavierStokes equations with wellprepared initial data in threedimensional bounded domains
(20111231)This paper studies the incompressible limit of the nonisentropic NavierStokes equations for viscous polytropic flows with zero thermal coefficient in threedimensional bounded C4domains. The uniform estimates in the ... 
Interface motion by interface diffusion driven by bulk energy: Justification of a diffusive interface model
(20111231)We construct an asymptotic solution of a system consisting of the partial differential equations of linear elasticity theory coupled with a degenerate parabolic equation, and show that when a regularity parameter tends to ... 
Internal control for nonlocal Schrodinger and wave equations involving the fractional Laplace operator
(, 20141231)We analyse the interior controllability problem for a nonlocal Schr\"odinger equation involving the fractional Laplace operator $(\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The ... 
Inverse problem for the heat equation and the Schrödinger equation on a tree
(20121231)In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a starshaped tree. The Carleman ... 
Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
(20101231)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 ... 
L ∞ variational problems for maps and the Aronsson PDE system
(20121231)By employing Aronsson's absolute minimizers of L ∞ functionals, we prove that absolutely minimizing maps u:Rn→RN solve a "tangential" Aronsson PDE system. By following Sheffield and Smart (2012) [24], we derive δ ∞ with ... 
Large Time Asymptotics for Partially Dissipative Hyperbolic Systems
(20111231)This work is concerned with (ncomponent) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using ... 
Largetime asymptotics, vanishing viscosity and numerics for 1D scalar conservation laws
(20141231)In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ... 
Largetime behavior of some numerical schemes: application to the sonicboom phenomenon
(20141210)In this thesis we highlight the necessity of employing numerical schemes that preserve the largetime dynamical properties of the continuous system. We focus on Burgers like equations, which are well known to develop ... 
Local Exact Controllability for the OneDimensional Compressible NavierStokes Equation
(20121231)In this paper we deal with the isentropic (compressible) NavierStokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions ... 
Localized solutions and filtering mechanisms for the discontinuous Galerkin semidiscretizations of the 1d wave equation [Solutions localisées et mécanismes de filtrage pour les approximations de Galerkin discontinues de l'équation des ondes.]
(20101231)We perform a complete Fourier analysis of the semidiscrete 1d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits ... 
Localized solutions for the finite difference semidiscretization of the wave equation [Solutions localisées pour la semidiscrétisation par différences finies de l'équation des ondes]
(20101231)We study the propagation properties of the solutions of the finite difference space semidiscrete wave equation on a uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that ...