From Particle Systems to Partial Differential Equations III: Particle Systems and PDEs III, Braga, Portugal, December 2014

Description

The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014.   The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations.  This book will appeal to probabilists, analysts and those mathematicians whose work involves topics in mathematical physics, stochastic processes and differential equations in general, as well as those physicists whose work centers on statistical mechanics and kinetic theory. Front Matter....Pages i-viii On Linear Hypocoercive BGK Models....Pages 1-37 Hydrodynamic Limit of Quantum Random Walks....Pages 39-50 Sub-shock Formation in Reacting Gas Mixtures....Pages 51-72 Compactness of Linearized Kinetic Operators....Pages 73-97 Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations....Pages 99-120 Entropy Dissipation Estimates for the Landau Equation: General Cross Sections....Pages 121-143 The Boltzmann Equation over \({{\mathbb R}^{{\mathrm {D}}}}\) : Dispersion Versus Dissipation....Pages 145-166 The Gradient Flow Approach to Hydrodynamic Limits for the Simple Exclusion Process....Pages 167-184 Symmetries and Martingales in a Stochastic Model for the Navier-Stokes Equation....Pages 185-194 Convergence of Diffusion-Drift Many Particle Systems in Probability Under a Sobolev Norm....Pages 195-223 From Market Data to Agent-Based Models and Stochastic Differential Equations....Pages 225-242 Global Asymptotic Stability of a General Nonautonomous Cohen-Grossberg Model with Unbounded Amplification Functions....Pages 243-262 Phase Transitions and Coarse-Graining for a System of Particles in the Continuum....Pages 263-283 Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators....Pages 285-300 Derivation of the Boltzmann Equation: Hard Spheres, Short-Range Potentials and Beyond....Pages 301-321 Duality Relations for the Periodic ASEP Conditioned on a Low Current....Pages 323-350