From Particle Systems to Partial Differential Equations

This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general, whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to those physicists who work in statistical mechanics and kinetic theory.

Deals with mathematical problems motivated by different applications in physics, engineering, economics, chemistry, and biology

R. Alonso, Brief discussion of the $L^{r}$-theory for the Boltzmann equation: cutoff and non-cutoff.- B. Anwasia, The Maxwell-Stefan Diffusion Limit of a Hard-Sphere Kinetic Model for Mixtures.- N. Ayi, An asymptotic preserving scheme for a stochastic linear kinetic equation in the diffusion regime.- C. Bahadoran, T. S. Mountford, K. Ravishankar and E. Saada C. Bahadoran, Zero-range process in random environment.- P. Birmpa, P. Gonçalves and D. Tsagkarogiannis, On non-equilibrium fluctuations for the Stirring process with births and deaths.- Erica de la Canal, Irene M. Gamba and M. Pavic-Colic, On existence, uniqueness and Banach space regularity for solutions of Boltzmann equations systems for monatomic gas mixtures.- P. Capitão and P. Gonçalves, Hydrodynamics of weakly asymmetric exclusion with slow boundary.- M. Fernanda P. Costa, M. Piedade M. Ramos, C. Ribeiro, A. J. Soares, Recent developments on the modelling of cell interactions in autoimmune diseases.- L. De Carlo, Geometrical structures of the instantaneous current and their macroscopic effects: vortices and perspectives in non-gradient models.- R. De Paula and C. Franceschini, Porous medium model: an algebraic perspective and the Fick's law.- G. dos Reis and V. Platonov, Forward utilities and Mean-field games under relative performance concerns.- S. Frómeta, R. Misturini and A. Neumann, The boundary driven zero-range process.- F. Golse, Partial Regularity in Time for the Landau Equation (with Coulomb Interaction).- M. Griffin-Pickering and M. Iacobelli, Recent developments on the well-posedness theory for Vlasov-type equations.- D. Karevski and G. M. Schutz, Charge-current correlation identities for stochastic interacting particle systems.- C. Saffirio, From the Hartree to the Vlasov dynamics: conditional strong convergence.- F. Salvarani, From the Boltzmann description for mixtures to the Maxwell-Stefan diffusion equations.- R. V. Mendes, Alternative quantum formulations and systems at the classical-quantum border.