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Now showing items 1-10 of 11

#### Numerical approximation of a one-dimensional elliptic optimal design problem

(2011-12-31)

We address the numerical approximation by finite-element 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, ...

#### On a nonlocal moving frame approximation of traveling waves

(2011-12-31)

The profiles of traveling wave solutions of a 1-d reaction-diffusion parabolic equation are transformed into equilibria of a nonlocal equation, by means of an appropriate nonlocal change of variables. In this new formulation ...

#### Switching control

(2011-12-31)

We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to another in a systematic way so that, at ...

#### Observability of heat processes by transmutation without geometric restrictions

(2011-12-31)

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] ...

#### 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]

(2011-12-31)

We build Gaussian wave packets for the linear Schrödinger equation and its finite difference space semi-discretization and illustrate the lack of uniform dispersive properties of the numerical solutions as established in ...

#### Sharp Observability Estimates for Heat Equations

(2011-12-31)

The goal of this article is to derive new estimates for the cost of observability of heat equations. We have developed a new method allowing one to show that when the corresponding wave equation is observable, the heat ...

#### Large Time Asymptotics for Partially Dissipative Hyperbolic Systems

(2011-12-31)

This work is concerned with (n-component) 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 ...

#### The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide

(2011-12-31)

We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay ...

#### On the regularity of null-controls of the linear 1-d heat equation [Sur la regularité des contrôles pour l'équation de la chaleur linéaire]

(2011-12-31)

The 1-d heat equation in a bounded interval is null-controllable from the boundary. More precisely, for each initial data y0εL2(0,1) there corresponds a unique boundary control of minimal L2(0,T)-norm which drives the state ...

#### Flux identification for 1-d scalar conservation laws in the presence of shocks

(2011-12-31)

We consider the problem of flux identification for 1-d scalar conservation laws formulating it as an optimal control problem. We introduce a new optimization strategy to compute numerical approximations of minimizing fluxes. ...