Browsing Past Topics (PT) by Title
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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 ... 
Long time dynamics of a multidimensional nonlinear lattice with memory
(20151231)This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction ... 
Long time versus steady state optimal control
(20131231)This paper analyzes the convergence of optimal control problems for an evolution equation in a finite timehorizon [0, T] toward the limit steady state ones as T ?8. We focus on linear problems. We first consider linear ... 
Low Mach number limit of viscous polytropic fluid flows
(20111231)This paper studies the singular limit of the nonisentropic NavierStokes equations with zero thermal coefficient in a twodimensional bounded domain as the Mach number goes to zero. A uniform existence result is obtained ... 
Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space
(20121231)We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u)=∫ ℝdK(x,y)(u(y)u(x))dy. Here we consider a kernel K(x, y)=ψ(ya(x))+ψ(xa(y)) where ψ is a bounded, nonnegative ... 
Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems
(20101231)A rigorous justification of several wellknown mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled NavierStokesFourier system, where some of the characteristic numbers ... 
Maximum Principles for vectorial approximate minimizers of nonconvex functionals
(20131231)We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance ... 
Minimization of length and curvature on planar curves
(20091231)In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional ∫ √1+K 2 ds, depending both on length and curvature K. We fix starting and ending points ...