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

Front Cover
Patrícia Gonçalves, Ana Jacinta Soares
Springer, Jul 16, 2016 - Mathematics - 350 pages

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.

 

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Contents

On Linear Hypocoercive BGK Models
1
Hydrodynamic Limit of Quantum Random Walks
38
Subshock Formation in Reacting Gas Mixtures
51
Compactness of Linearized Kinetic Operators
73
Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations
99
General Cross Sections
121
Dispersion Versus Dissipation
144
The Gradient Flow Approach to Hydrodynamic Limits for the Simple Exclusion Process
167
Convergence of DiffusionDrift Many Particle Systems in Probability Under a Sobolev Norm
195
From Market Data to AgentBased Models and Stochastic Differential Equations
225
Global Asymptotic Stability of a General Nonautonomous CohenGrossberg Model with Unbounded Amplification Functions
243
Phase Transitions and CoarseGraining for a System of Particles in the Continuum
263
Measuring Small Sets in the Presence of Elliptic Operators
284
Hard Spheres ShortRange Potentials and Beyond
301
Duality Relations for the Periodic ASEP Conditioned on a Low Current
323
Copyright

Symmetries and Martingales in a Stochastic Model for the NavierStokes Equation
185

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