RECENT ADVANCES IN KINETIC EQUATIONS AND APPLICATIONS

Université Pierre et Marie Curie, Paris, France

June 1st, 2016

Scientific and organizing committee:

L. Boudin, F. Golse, F. Salvarani

Registration:

Registration is free but compulsory. The inscriptions are now closed.

Program:

9h50-10h Opening (L. Boudin, F. Golse, F. Salvarani)
10h00-10h50 L. Desvillettes
10h50-11h20 Coffee break
11h20-12h10 S. Méléard
12h10-13h00 C. Mouhot

14h30-15h20 S. Serfaty
15h20-16h10 C. Bardos
16h10-16h40 Coffee break
16h40-17h30 C. Villani

18h00 Cocktail

Venue:

UPMC, Jussieu campus, room 15.25.104, 1st floor, access by tower 15.
To reach the UPMC Jussieu campus, please check this webpage:
http://www.upmc.fr/fr/universite/campus_et_sites/a_paris_et_en_idf/jussieu.html

Titles and abstracts:

Claude Bardos: About Boltzmann-Maxwell relation and multiscale analysis

Abstract

Laurent Desvillettes: Robustness of Boltzmann's H Theorem

Abstract: The case of equality in Boltmann's H Theorem (of rarefied monoatomic gases) consists in solving a functional equation for the density in phase space of a gas at thermodynamical equilibrium. A variant of the original proof of Boltzmann enables to state robustness results leading to extensions of the H Theorem which are useful for various models appearing in physics.

Sylvie Méléard: From evolutionary ecology to nonlinear fractional reaction-diffusion equations

Abstract: We are interested in modeling Darwinian evolution  resulting from the interplay of phenotypic variation and natural selection through ecological interactions.
The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. In the case we are interested in, the probability distribution of mutations has a  heavy tail and belongs to the  domain of  attraction of a stable law.  We investigate the large-population limit with allometric demographies and derive a reaction-diffusion equation with fractional Laplacian and nonlocal nonlinearity. We then study a singular limit when the diffusion is assumed to be small. With a rescaling which differs from the classical one in the Laplacian case, we obtain a particular class of Hamilton-Jacobi equations in the limit. This singular limit has an interpretation in the biological framework of adaptive dynamics.

Clément Mouhot: Landau damping in the whole space in finite regularity

Sylvia Serfaty: Mean Field Limits for Ginzburg-Landau vortices

Abstract: Ginzburg-Landau type equations are models for superconductivity, superfluidity, Bose-Einstein condensation, etc. A crucial feature is the presence of quantized vortices, which are topological zeroes of the complex-valued solutions. We will present a new result on the derivation of a mean-field limit equation for the dynamics of many vortices starting from the parabolic Ginzburg-Landau equation or the Gross-Pitaevskii (= Schrödinger Ginzburg-Landau) equation.

Cédric Villani: TBA

Poster of the workshop