Browsing Past Topics (PT) by Issue Date
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Some controllability results for the 2D Kolmogorov equation
(20091231)In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the righthand side of the equation, located on a subdomain, that ... 
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 ... 
Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order
(20091231)In the present article we first study the existence of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order, which was proposed by Mullins ["Twodimensional motion of idealized ... 
Uniformly exponentially stable approximations for a class of damped systems
(20091231)We consider time semidiscrete approximations of a class of exponentially stable infinitedimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semidiscrete systems, due ... 
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 ... 
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 ... 
Stabilization of the wave equation on 1D networks
(20091231)In this paper we study the stabilization of the wa ve equation on general 1d networks. For that, we transfer known observability results in the context of control problems of conservative systems (see [R. Dáger and E. ... 
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: ... 
2D euler shape design on nonregular flows using adjoint rankinehugoniot relations
(20091231)Optimal aerodynamic shape design aims to find the minimum of a functional that describes an aerodynamic property, by controlling the partial differential equation modeling the dynamics of the flow that surrounds an aircraft, ... 
Convergence of a twogrid algorithm for the control of the wave equation
(20091231)We analyze the problem of boundary observability of the finitedifference space semidiscretizations of the 2d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ... 
Time discrete wave equations: Boundary observability and control
(20091231)In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable ... 
Asymptotic stability of rarefaction wave for the navierstokes equations for a compressible fluid in the half space
(20091231)This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the NavierStokes equations in a compressible fluid in the Eulerian coordinate in the half space. ... 
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 ... 
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 ... 
Asymptotic limits and stabilization for the 1D nonlinear MindlinTimoshenko system
(20101231)This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
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 ... 
Strichartz estimates for the Schrödinger equation on a tree and applications
(20101231)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 Strichartzlike estimates for the linear semigroup and apply them to ... 
Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach
(20101231)In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space ... 
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 ... 
A systematic method for building smooth controls for smooth data
(20101231)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 ...