From Particle Systems to Partial Differential Equations

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology.

Inhalt

Thierry Paul, Mario Pulvirenti and Sergio Simonella, Mean Field Limit for the Kac model and Grand Canonical Formalism.- L. Desvillettes, Some remarks about the Link between the Fisher information and Landau or Landau-Fermi-Dirac entropy dissipation.- Rossana Marra, Hydrodynamic limit from the Boltzmann equation in a slightly compressible regime.- Amit Einav, The Entropic journey of Kac's Model.- L. S. Ferreira, Entropy production bounds for the Kac model are uniform in the number of particles.- P. Degond, Radial Laplacian on rotation groups.- Bernt Wennberg, The two dimensional Lorentz gas in the kinetic limit: theoretical and numerical results.- F. Bonetto, E. A. Carlen, L. Hauger, and M. Loss, Approach to equilibrium for the Kac model.- L. Laeche and C. Sario, Uniqueness criteria for the VlasovPoisson system and applications to semiclassical analysis.- Yuri G. Kondratiev, T. Kuna, M. J. Oliveira, J. L. da Silva, and L. Streit, Results about the free Kawasaki dynamics of continuous particle systems in innite volume: long-time asymptotics and hydrodynamic limit.- R. Vilela Mendes, Intemperate Levy processes and white noises.- G. M. Schutz, Mesoscale mode coupling theory for the weakly asymmetric simple exclusion process.- F. Salvarani, The extended phase space method in kinetic theory.- F. Golse, Quantum Wasserstein and Observability for Quantum Dynamics.- E. A. Carlen, A. Novick-Cohen, and L. P. Hari, Connecting the Deep Quench Obstacle Problem with Surface Diffusion via their Steady States.- F. Achleitner, A. Arnold, and A. Jungel, Necessary and sufcient conditions for strong stability of explicit RungeKutta methods.- V. Ricci and B. Coppi and R. Spigler, Magnetic reconnection: some basic ideas and a review on a collisionless model.