Mathematical methods for hydrodynamic limits
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 dy...
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| Main Authors | , |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Berlin, Heidelberg
Springer-Verlag
1991
Springer Berlin / Heidelberg Springer Berlin Heidelberg Springer |
| Edition | 1 |
| Series | Lecture Notes in Mathematics |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9783540550044 0387550046 9780387550046 3540550046 9783662203255 3662203251 |
| ISSN | 0075-8434 1617-9692 |
| DOI | 10.1007/BFb0086457 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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. |
| Author | De Masi, Anna Presutti, Errico |
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| Notes | Includes index Bibliographical references: p. [189]-194 |
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| Snippet | Entropy inequalities, correlation functions, couplingsbetween stochastic processes are powerful techniques whichhave been extensively used to give arigorous... Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous... Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous... |
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| SubjectTerms | Complex Systems Distribution (Probability theory Mathematics Mathematics and Statistics Percolation (Statistical physics) Probability Theory and Stochastic Processes Statistical physics Statistical Physics and Dynamical Systems |
| TableOfContents | Hydrodynamic limits for independent particles -- Hydrodynamics of the zero range process -- Particle models for reaction-diffusion equations -- Particle models for the Carleman equation -- The Glauber+Kawasaki process -- Hydrodynamic limits in kinetic models -- Phase separation and interface dynamics -- Escape from an unstable equilibrium -- Estimates on the V-functions. |
| Title | Mathematical methods for hydrodynamic limits |
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