Congrès d'Analyse Numérique pour les Jeunes - 2020

Session

Session parallèle 10

11

4 déc. 2020, 14:00

Zoom (Virtuel)

Description

CLIQUER ICI POUR REJOINDRE LA SALLE 2

Président.e de session : Mathilde Boissier

Modérateur.trice : Matthieu Aussal

17. Contrôlabilité de systèmes linéaires paraboliques avec contrainte de positivité sur l'état

Clément Moreau (CEREMADE, Université Paris-Dauphine PSL)

04/12/2020 14:00

Soit $N,m,d\in {\mathbb{N}}^{\ast }$, $\mathrm{\Omega }$ un ouvert borné régulier de ${\mathbb{R}}^d$, $\omega$ un ouvert inclus dans $\mathrm{\Omega }$ et $T>0$. On considère un système linéaire parabolique de $N$ équations couplées avec contrôle interne sur $\omega$, de la forme
$$
\tag{1} \left {
\begin{array}{l l l}
\partial_t Y - D \Delta Y &= A Y + B u \mathbf{1}_{\omega} &\text{sur } \Omega_T,...

38. Exponential BV stability for networks of scalar conservation laws

Mathias Dus (Institut des mathématiques de Toulouse)

04/12/2020 14:30

In this presentation, we will talk about networks of $d\in \mathbb{N}$ scalar conservation laws with positive characteristic velocities. The interaction takes place at the boundary, where a feedback operator acts. The open loop system is given below with $H$ a square matrix given by the physics having a destabilizing effect:

\begin{equation}
\left{
\begin{array}{lll}
R_t + [f(R)]_x &=&...

48. A penalty approach to the LQR optimal control problem for the Boussinesq system

Kévin Le Balc'h (IMB)

04/12/2020 15:00

We consider the infinite time horizon LQR optimal control problem for the linearized Boussinesq system. The goal is to justify the approximation by penalization of the free divergence condition in this context. More precisely, under suitable assumptions, we establish convergence results for optimal controls, optimal solutions and Riccati operators when the penalization parameter goes to zero.

37. A symmetric algorithm for solving mechanical contact problems using FreeFEM

M. Houssam Houssein (LJLL - Sorbonne Université)

04/12/2020 15:30

The mechanical Contact between two bodies is one of the most difficult problems in solid mechanics, indeed the material non-linearity must be taken into account and the contact area is unknown. In the case of frictional contact another non-linearity must be considered and makes the problem even more difficult. There exist several algorithms to solve the contact problems [3], most of them...

52. Targeted immunization strategies

Dylan Dronnier (CERMCIS)

04/12/2020 16:00

In an homogeneous population, the basic reproduction number of an infection, denoted by $R_0$, has originally been defined as the number of cases one individual generates on average over the course of its infectious period, in an otherwise uninfected population. This number plays a fundamental role in epidemiology as it provides a scale to measure how difficult to control an infectious...