Colloque sur des questions liées aux EDP.

Calais le 23 mai 2019.





Program.

10h:   Antoine Benoit (Université du Littoral Côte d'Opale, LMPA): Problèmes aux limites hyperboliques dans une bande : caractère SE fortement bien posé et développements BKW.

Abstract: Dans cet exposé on considérera des systèmes d'équations hyperboliques posés dans une bande en espace. Une question naturelle pour de tels problèmes est alors de déterminer les conditions de bords conduisant au caractère fortement bien posé (existence, unicité et estimation d'énergie de la solution). Une telle caractérisation a été établie par Kreiss en 1970 dans le cas du demi-espace et repose sur la condition dite de Kreiss-Lopatinskii uniforme (KLU). En ce qui concerne le problème dans la bande on verra dans une première partie qu'une nouvelle condition (en plus de la condition KLU) est nécessaire et suffisante pour assurer le caractère fortement bien posé et contrôler la croissance temporelle de la solution. Toutefois cette condition est très peu explicite. C'est pourquoi dans une seconde partie on essayera de donner des propriétés qualitatives de cette condition grâce à des techniques de type développements d'optique géométrique.


11h:  Antoine Zurek (Université de Lille, LPP): Analysis of a finite-volume scheme for a cross-diffusion system modeling biofilm growth.

Abstract: Biofilms are organized cooperating communities of microorganisms. Typically biofilms consist of several species such that multicomponent fluid models have to be considered. Recently a model consisting of a system of parabolic equations with cross-diffusion has been proposed.
In this talk I will introduce and analyze a finite volume scheme which preserves the structure of that system. The scheme consists of an Euler discretization in time and a two-point flux approximation in space. I will prove the existence of solutions to that scheme with nonnegative discrete densities and a discrete total biomass for all control volumes. Also I will discuss the convergence of the scheme and the long-time behavior of the solutions to the discrete problem. Finally I will present some numerical experiments.



12h - 14h: Repas.


14h:  Vivien Desveaux (Université de Picardie Jules Verne, LAMFA): Un modèle 1D d'écoulement sanguin dans les artères.

Abstract: L'écoulement du sang dans les artères est modélisé par les équations de Navier-Stokes 3D, avec une force de rappel élastique pour la paroi. Cela s'avère extrêmement coûteux lorsque l'on veut simuler tout un réseau. En intégrant sur la section transverse de l'artère et en faisant certaines hypothèses simplificatrices, on peut obtenir un modèle 1D plus simple sous la forme d'un système hyperbolique d'EDP. Dans cet exposé, j'expliquerai d'abord comment on obtient ce modèle à partir de Navier-Stokes, avant de donner ses principales propriétés. Je proposerai ensuite une mtéthode numérique pour approcher les solutions, ainsi qu'une extension à l'ordre 2. On verra que le schéma construit vérifie plusieurs propriétés importantes (robustesse, préservation des états d'équilibre,...). Je terminerai en présentant quelques résultats numériques illustrant ces propriétés.


15h:  Benjamin Melinand (Université Paris-Dauphine, CEREMADE): Stability of steady viscous conservation laws solutions on a finite interval.

Abstract: In this talk I will explain how one can show the nonlinear stability of steady solutions of viscous conservation laws. It is a two-step process. First, one has to study the linearized problem about the steady state. It is mostly a spectral analysis and we use a well-chosen analytic function called the Evans function. Secondly, one must show how the linear stability implies the nonlinear stability. This is based on appropriate energy estimates.




Where in Calais will the conference take place?

The conference will take place in room B014 on the campus "la Mi-Voix" of the Université du Littoral.

This room is located in the ground floor of the building connected to the low, round, red-brick tower on the campus (see below). When you enter this tower, B014 is the first room on the right-hand side.

Image of the building where the conference will take place.



How to get from the train station to the university.

There are two bus lines you may use. The first is line 4. You may take a bus of this line at the train station in the direction "Utrillo". Departure times are, for example, 8:10, 8:32, 8:52, 9:11, 9:40, 9:53, 10:02, 10:22, 10:43.

Expect a ride of about 15 minutes; the bus takes a very circuitous route through Calais. Leave the bus at the station "Vadez". You will find yourself at a four-lane street with a channel in the middle. The round, red-brick tower of the campus "la Mi-Voix" may be seen on the other side of the street. Follow the direction of the bus for about 100 m, then take the footbridge over the channel and go back to the red tower.

The other bus line you may take is line 2. Buses of this line also stop at the train station. The direction you have to choose is "C Cial Mi-Voix" ("Centre Commercial de la Mi-Voix"). Departure times are, for example, 8:05, 8:22, 8:44, 9:06, 9:28, 9:50.

Also expect a ride of about 15 minutes, although on a completely different route. Leave the bus at the stop "Grande Rue" (which actually is a rather narrow street). From there walk about 300 m straight further on in the direction the bus was driving when it arrived at the stop. Then you come to a roundabout, where you should turn right and go to the red-brick tower (200 m). The walking distance is longer than if you take the bus number 4.

If you like to walk from the train station to the university, here is a route -- about 2 km long (30 minutes): Take the street in front of the train station in the direction of City Hall ("Hotel de Ville") (left-hand side when you stand in front of the station, with your back to it). Cross the car park in front of City Hall, turn left and follow the rue Jean Jaurès for about 150 m. Then you come to a channel; turn right and follow this channel up to the lift bridge. There turn left and go over that bridge. Then, starting from the roundabout behind the bridge, you have to walk straight on, in a right angle to the channel, for about 1 km (avenue de Blériot). When reaching the traffic lights at the end of that kilometer, go straight on, across the street and across the bridge over the channel you find there. The "Centre Universitaire de la Mi-Voix" is on the left-hand side in front of you. Head for the low, round, red-brick tower at its distant right corner.

If you want to take a taxi from the train station to the university, ask to go to the "Restaurant Universitaire". It is located just in front of the red-brick tower. A ride costs about 8 euro.






Dernière mise à jour de ce site le 6 mai 2019.