Mathematical Methods for Hydrodynamic Limits by Errico Presutti, Anna DeMasi
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Format Paperback
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Description Discretevelocity Boltzmann equations, reaction diffusionequations and non linear parabolic equations are considered,as limits of particles models.
Publisher Description
Entropy inequalities, correlation functions, couplingsbetween stochastic processes are powerful techniques whichhave been extensively used to give arigorous foundation tothe theory of complex, many component systems and to itsmany applications in a variety of fields as physics,biology, population dynamics, economics, ...The purpose of the book is to make theseand othermathematical methods accessible to readers with a limitedbackground in probability and physics by examining in detaila few models where the techniques emerge clearly, whileextra difficulties arekept to a minimum.Lanford's method and its extension to the hierarchy ofequations for the truncated correlation functions, thev-functions, are presented and applied to prove the validityof macroscopic equations forstochastic particle systemswhich are perturbations of the independent and of thesymmetric simple exclusion processes. Entropy inequalitiesare discussed in the frame of the Guo-Papanicolaou-Varadhantechnique and of theKipnis-Olla-Varadhan super exponentialestimates, with reference to zero-range models. Discretevelocity Boltzmann equations, reaction diffusionequations and non linear parabolic equations are considered,as limits of particles models. Phase separation phenomenaare discussed in the context of Glauber+Kawasaki evolutionsand reaction diffusion equations. Although the emphasis isonthe mathematical aspects, the physical motivations areexplained through theanalysis of the single models, withoutattempting, however to survey the entire subject ofhydrodynamical limits.
Details ISBN 3540550046 ISBN-13 9783540550044 Title Mathematical Methods for Hydrodynamic Limits Author Errico Presutti, Anna DeMasi Format Paperback Year 1992 Pages 196 Edition 1991st Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG GE_Item_ID:140535259; About Us
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