Seminars take place in the seminar room, first floor of the building Le Chablais, (see How to come ?).

Next seminar:

Friday 3rd May 2019 at 14h Friedemann Brock (University Swansea),
Isoperimetric inequalities w.r.t. homogeneous weights and symmetry of optimal functions in CKN inequalities

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.
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Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, all years together.

Year 2019

Saturday 23rd November 2019 at 14h Paolo Salani (Univeresite de Florence),
à venir

Friday 17th May 2019 at 14h Alessandro Duca (Univ Grenoble Alpes, IF),
Controllability of localized quantum states on infinite graphs through bilinear control fields

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We consider a particle constrained in a graph structure and excited by an external controlling field. Its dynamics is modeled by the bilinear Schrödinger equation i∂t ψ = −∆ψ + u(t)Bψ in the Hilbert space L2(G , C) where G is the graph. The Laplacian −∆ is equipped with self-adjoint boundary conditions. The action of the field is represented by the bounded symmetric operator B and by the control function u ∈ L2((0,T),R) with T > 0, which accounts its intensity. The exact controllability of the bilinear Schrödinger equation on bounded intervals was widely studied in literature. Nevertheless, the bilinear Schrödinger equation on graphs is in general a more delicate matter and it was only studied on compact networks. Up to our knowledge, the controllability on infinite graphs is still an open problem. The main reason can be found on the dispersive phenomena characterizing the equation (not considering the difficulties already appearing on compact graphs). A peculiarity of the Schrödinger equation is the loss of localization of the wave packets during the evolution, the dispersion. This effect can be measured by L ∞ -time decay. In this talk, we present the bilinear Schrödinger equation on infinite graphs. In par- ticular, we show the existence of suitable subspaces of L 2 (G , C) where the equation is well-posed. In such spaces, we define assumptions on the structure of the graph and on the control field such that the global exact controllability is guaranteed. The result leads to the so-called “energetic controllability”.

Friday 3rd May 2019 at 14h Friedemann Brock (University Swansea),
Isoperimetric inequalities w.r.t. homogeneous weights and symmetry of optimal functions in CKN inequalities

Friday 5th April 2019 at 14h Mark Ashbaugh (University of Missouri),
Isoperimetric and Universal Inequalities in Geometry and Physics

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This talk will survey some of the interesting inequalities that arise from the interplay between geometry, analysis, and mathematical physics. Discussions of the classical isoperimetric inequality (given a length of string, how do you arrange it to enclose the most area?) and the eigenvalue problem for a symmetric matrix will set the stage. The main focus of the talk will be on the eigenvalues of various differential operators, especially the Laplacian including its one-dimensional specialization, -d^2/dx^2. In physical terms, the eigenvalues of these differential operators give the natural frequencies of vibrating strings and drums. The analog of the classical isoperimetric inequality for the Laplacian is called the Faber-Krahn inequality, which states that among all drums of a given area the one producing the lowest bass note is the circular one (all other physical parameters held fixed). By analogy, we call such an analytic inequality an {it isoperimetric inequality}. Such results, when the optimizing case is a disk or ball, are usually proved via symmetrization (rearrangement) techniques, which we will sketch. Beyond that there are many interesting general inequalities for eigenvalues, several of which can be proved by elementary means. We look at a few of these inequalities, such as inequalities relating the Dirichlet and Neumann eigenvalues of the Laplacian and also the {it universal eigenvalue inequalities} of Payne, P'olya, and Weinberger (PPW) and their successors, which are inequalities between the eigenvalues of the Dirichlet Laplacian and give control over their rate of growth.

Friday 29th March 2019 at 14h Dimitrios Mitsotakis (Victoria University of Wellington (New Zeland)),
Numerical solution of the Serre equations for strongly-nonlinear surface water waves

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We solve numerically the Serre-Green-Naghdi (SGN) system using stable, accurate and efficient fully discrete numerical schemes based on Galerkin/finite element methods. After reviewing the properties of the SGN system we present the convergence properties of the numerical scheme. A detailed study of the dynamics of the solitary waves of the SGN system over variable bottom topographies is also presented. It is noted that the Galerkin/finite element method is the only method analytically proven to be convergent for the numerical solution of the Serre equations so far.

Friday 8th March 2019 at 14h Joachim Bernier (ENS Rennes, IRMAR),
Formes normales rationnelles et stabilité des petites solutions des équations de Schrödinger non linéaires

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En l’absence de potentiel, les équations de Schrödinger non linéaires (NLS) sont des équations résonnantes. En particulier, la théorie des formes normales de Birkhoff ne garantie pas la stabilité des petites solutions de NLS sur des temps très longs. Cependant, sur le tore de dimension 1, la partie cubique de la non-linéarité ne contient aucun terme résonnant non-trivial. En partant de cette observation, on verra comment construire une nouvelle famille de formes normales permettant de conjuguer, sur de gros ensembles de petites fonctions régulières, la dynamique de NLS à une dynamique stable (et intégrable) sur des temps très longs.

Friday 15th February 2019 at 14h Rebecca Tyson (Univ british Columbia),
Prédiction de la dispersion de pollen transgénique

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La prévention d'une trop grande dispersion de pollens transgéniques est un sujet de grande importance dans l'agriculture moderne. Le mouvement du pollen transgénique se fait en grande partie par des insectes pollinisateurs, dont le plus important est l'abeille domestique, apis mellifera. Dans cet exposé, je vais présenter des modèles mathématiques pour le mouvement des abeilles, et montrer comment ces modèles peuvent nous aider à prédire la dispersion du pollen transgénique.

Friday 25th January 2019 at 14h Thierry Gallay (Institut Fourier UGA),
Stabilité spectrale des colonnes de tourbillon

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On étudie la stabilité d'une famille de solutions stationnaires de l'équation d'Euler dans R^3 qui décrivent des tourbillons à symétrie cylindrique : le champ de vitesse est dans le plan horizontal, et ne dépend que de la distance à l'axe vertical. Ces solutions ont été étudiées notamment par Kelvin et Rayleigh au 19ème siècle, mais les seuls résultats de stabilité obtenus jusqu'ici concernent des perturbations très particulières (bidimensionnelles ou axisymétriques). On donne une condition suffisante sur le profil de vitesse du tourbillon garantissant la stabilité spectrale vis-à-vis de perturbations arbitraires. Il s'agit d'un travail en collaborationa avec Didier Smets

Friday 18th January 2019 at 14h Jiao He (ICJ, Univ Lyon 1),
Évanescence d'un petit solide dans un fluide visqueux incompressible

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Dans cet exposé, je présenterai un problème qui modélise le mouvement d'un solide dans un fluide visqueux incompressible. On s'intéresse ici à l'évolution d'un seul obstacle qui se rétrécit en une particule ponctuelle dans un fluide de R^2 ou R^3. On montrera la convergence des solutions du système fluide-solide vers une solution des équations de Navier-Stokes sans obstacle grâce aux estimations d'énergie.

The seminar of the team EDPs² is under the responsibility of Jimmy Garnier.
Settings: See with increasing date . Hide abstracts
Other years: 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, all years together.