Browsing Past Topics (PT) by Title
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Nematic elastomers: Gammalimits for large bodies and small particles
(20111231)We compute the largebody and the smallparticle Gammalimit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and ... 
Nonreflecting boundary condition on ellipsoidal boundary
(20121231)The modeling of wave propagation problems using finite element methods usually requires the truncation of the computation domain around the scatterer of interest. Absorbing boundary conditions are classically considered ... 
Nonlinear weakly curved rod by ΓConvergence
(20121231)We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the crosssection. We use an approach analogous to the one for rods and curved rods ... 
Null controllability for a heat equation with a singular inversesquare potential involving the distance to the boundary function
(20160101)This article is devoted to the analysis of control properties for a heat equation with a singular potential μ/δ2, defined on a bounded C2 domain Ω⊂RN, where δ is the distance to the boundary function. More precisely, we ... 
Null controllability for some systems of two backward stochastic heat equations with one control force
(20121231)The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for ... 
Null controllability of a degenerated reactiondiffusion system in cardiac electrophysiology [Nulle contrôlabilité d'un système dégénéré de réactiondiffusion dans l'électiquephysiologie du cœur]
(20121231)This Note is devoted to the analysis of the null controllability of a nonlinear reactiondiffusion system, approximating a parabolicelliptic system, modeling electrical activity in the heart. The uniform, with respect to ... 
Null controllability of a system of viscoelasticity with a moving control
(20141231)In this paper, we consider the wave equation with both viscous KelvinVoigt and frictional damping as a model of viscoelasticity in which we incorporate an internal control with a moving support. We prove the null ... 
Null controllability of viscous HamiltonJacobi equations
(20121231)We study the problem of null controllability for viscous HamiltonJacobi equations in bounded domains of the Euclidean space in any space dimension and with controls localized in an arbitrary open nonempty subset of the ... 
Numerical approximation of a onedimensional elliptic optimal design problem
(20111231)We address the numerical approximation by finiteelement methods of an optimal design problem for a two phase material in one space dimension. This problem, in the continuous setting, due to high frequency oscillations, ... 
Numerical approximation of null controls for the heat equation : Illposedness and remedies
(20101231)The numerical approximation of exact or trajectory controls for the wave equation is known to be a delicate issue, since the pioneering work of GlowinskiLions in the nineties, because of the anomalous behavior of the ... 
Numerical approximation schemes for multidimensional wave equations in asymmetric spaces
(20151231)We develop finite difference numerical schemes for a model arising in multibody structures, previously analyzed by H. Koch and E. Zuazua, constituted by two ndimensional wave equations coupled with a (n  1) dimensional ... 
Numerical aspects of largetime optimal control of Burgers equation
(20151013)In this paper, we discuss the efficiency of various numerical methods for the inverse design of the Burgers equation, both in the viscous and in the inviscid case, in long timehorizons. Roughly, the problem consists in, ... 
Numerical dispersive schemes for the nonlinear Schrödinger equation
(20091231)We consider semidiscrete approximation schemes for the linear Schrödinger equation and analyze whether the classical dispersive properties of the continuous model hold for these approximations. For the conservative finite ... 
Numerical meshes ensuring uniform observability of onedimensional waves: Construction and analysis
(20160101)We build nonuniform numerical meshes for the finite difference and finite element approximations of the onedimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ... 
Observability estimate for stochastic Schrödinger equations and its applications
(20131231)In this paper, we establish a boundary observability estimate for stochastic Schrödinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic ... 
Observability of heat processes by transmutation without geometric restrictions
(20111231)The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] ... 
On a nonlocal moving frame approximation of traveling waves
(20111231)The profiles of traveling wave solutions of a 1d reactiondiffusion parabolic equation are transformed into equilibria of a nonlocal equation, by means of an appropriate nonlocal change of variables. In this new formulation ... 
On an extension of a bilinear functional on Lp(Rd)⊗E to a Bochner space with an application to velocity averaging
(20131231)We examine necessary and sufficient conditions under which a continuous bilinear functional B on Lp(Rd)⊗E, p>1, E being a separable Banach space, can be continuously extended to a linear functional on Lp(Rd;E). The ... 
On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients
(20141231)We study an optimal boundary control problem (OCP) associated to a linear elliptic equation div (‚àáy + A(x)‚àáy) = f. The characteristic feature of this equation is the fact that the matrix A(x) = [aij (x)] i;j=1; 
On Hardy inequalities with singularities on the boundary [Sur les inégalités de Hardy avec des singularités sur la frontière]
(20111231)In this Note we present some HardyPoincaré inequalities with one singularity localized on the boundary of a smooth domain. Then, we consider conical domains in dimension N≥3 whose vertex is on the singularity and we show ...