From Particle Systems to Partial Differential Equations

"This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic basic terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho's Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations.

The book will be of great interest to probabilists, analysts, and all mathematicians whose work focuses on topics in mathematical physics, stochastic processes and differential equations in general, as well as physicists working in statistical mechanics and kinetic theory.

Includes supplementary material: sn.pub/extras

Inhalt
Xavier Carvajal and Mahendra Panthee, A note on local well-posedness of generalized KdV type equations with dissipative perturbations.- Eduard Feireisl, Jií Mikyka, Hana Petzeltová, and Peter Taká, On the motion of chemically reacting fluids through porous medium.- Klemens Fellner and Bao Quoc Tang, Entropy methods and convergence to equilibrium for volume-surface reaction-diffusion systems.- R. Vilela Mendes, Ultradistribution spaces: Superprocesses and nonlinear differential problems.- François Golse, From the N-Body Schrödinger Equation to the Vlasov Equation.- Silvia Caprino, On a Vlasov-Poisson plasma with infinite charge and velocities.- Chi Hin Chan and Alexis Vasseur, De Giorgi techniques applied to the Hölder regularity of solutions to Hamilton-Jacobi equations.- Filipe Carvalho, A kinetic approach to steady detonation waves and their linear stability.- Roberto Monaco and Ana Jacinta Soares, A new mathematical model for environmental monitoring and assessment.- Valeria Ricci, Derivation of models for thin sprays from a multiphase Boltzmann model.- Jean-Christophe Mourrat, Hendrik Weber and Weijun Xu, Construction of F4/3 diagrams for pedestrians.- Tertuliano Franco, Patrícia Gonçalves and Adriana Neumann, Equilibrium uctuations for the slow boundary exclusion process.- Franz Achleitner, Two classes of nonlocal Evolution Equations related by a shared TravelingWave Problem.- D. Karevski, V. Popkov, G.M. Schütz, Matrix product ansatz for non-equilibrium quantum steady states.