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Now showing items 1-10 of 13

#### Some controllability results for the 2D Kolmogorov equation

(2009-12-31)

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 right-hand side of the equation, located on a subdomain, that ...

#### Hardy inequalities, observability, and control for the wave and schrödinger equations with singular potentials

(2009-12-31)

We address the question of exact controllability of the wave and Schrodinger equa\-tions perturbed by a singular inverse-square 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

(2009-12-31)

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 ["Two-dimensional motion of idealized ...

#### Uniformly exponentially stable approximations for a class of damped systems

(2009-12-31)

We consider time semi-discrete approximations of a class of exponentially stable infinite-dimensional systems modeling, for instance, damped vibrations. It has recently been proved that for time semi-discrete systems, due ...

#### Numerical dispersive schemes for the nonlinear Schrödinger equation

(2009-12-31)

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

(2009-12-31)

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 1-D networks

(2009-12-31)

In this paper we study the stabilization of the wa ve equation on general 1-d 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

(2009-12-31)

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: ...

#### 2-D euler shape design on nonregular flows using adjoint rankine-hugoniot relations

(2009-12-31)

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 two-grid algorithm for the control of the wave equation

(2009-12-31)

We analyze the problem of boundary observability of the finite-difference space semidiscretizations of the 2-d wave equation in the square.We prove the uniform (with respect to the meshsize) boundary observability for the ...