This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012.
The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory and to stimulate discussions and possibly new collaborations among researchers with different backgrounds.
The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navier-Stokes) from the Boltzmann equation, and several short papers written by some of the participants in the conference. Among the topics covered by the short papers are hydrodynamic limits; fluctuations; phase transitions; motions of shocks and anti shocks in exclusion processes; large number asymptotics for systems with self-consistent coupling; quasi-variational inequalities; unique continuation properties for PDEs and others.
The book will benefit probabilists, analysts and mathematicians who are interested in statistical physics, stochastic processes, partial differential equations and kinetics theory, along with physicists.
Table of Contents
Mini-Course: Fluid dynamic Limits of the Kinetic theory of gases : F. Golse.- Short Papers: Stationary quasivariational inequalities with gradient constraint and nonhomogeneous boundary conditions:A. Azevedo, F. Miranda, and L. Santos.- Shocks and antishocks in the ASEP conditioned on a low current: V. Belitsky and G.M. Schütz.- Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise: C. Bernardin.- Equilibrium fluctuations of additive functionals of zero-range models: C. Bernardin, P. Gonçalves, and S. Sethuraman.- A survey on Bogoliubov generating functionals for interacting particle systems in the continuum: D.L. Finkelshtein and M. João Oliveira.- Interacting particle systems: hydrodynamic limit versus high density limit: T. Franco.- Slowed exclusion process: hydrodynamics, fluctuations and phase transitions: T. Franco, P. Gonçalves, and A. Neumann.- Exclusion and Zero-range in the rarefaction fan: P. Gonçalves.- Microscopic derivation of an isothermal thermodynamic transformation: S. Olla.- Unique continuation property for the Benjamin equation: M. Panthee.- On the kinetic systems for simple reacting spheres: modeling and linearized equations: F. Carvalho, J. Polewczak, and A. Jacinta Soares.- Hydrodynamic Limit for the Velocity-flip Model: M. Simon.- Large number asymptotics for two–component systems with self–consistent coupling: V. Ricci.- On a stochastic coupled system of reaction-diffusion of nonlocal type: E.A. Coayla-Terán, J. Ferreira, P.M.D. de Magalhães, and H. B. de Oliveira.