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Mathematical Methods for Hydrodynamic Limits

  • Authors
  • Anna De Masi
  • Errico Presutti

Part of the Lecture Notes in Mathematics book series (LNM, volume 1501)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Anna De Masi, Errico Presutti
    Pages 1-6
  3. Anna De Masi, Errico Presutti
    Pages 7-32
  4. Anna De Masi, Errico Presutti
    Pages 33-51
  5. Anna De Masi, Errico Presutti
    Pages 52-66
  6. Anna De Masi, Errico Presutti
    Pages 67-96
  7. Anna De Masi, Errico Presutti
    Pages 97-111
  8. Anna De Masi, Errico Presutti
    Pages 112-127
  9. Anna De Masi, Errico Presutti
    Pages 128-146
  10. Anna De Masi, Errico Presutti
    Pages 147-166
  11. Anna De Masi, Errico Presutti
    Pages 167-188
  12. Back Matter
    Pages 189-196

About this book

Introduction

Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.

Keywords

Continuum limits Interacting particle systems Non linear Partial Differential Equations Propagation of chaos Statistical Mechanics Stochastic processes stochastic process

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0086457
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55004-4
  • Online ISBN 978-3-540-46636-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site