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Stochastic Porous Media Equations de Viorel Barbu

Stochastic Porous Media Equations: Lecture Notes in Mathematics, cartea 2163

Autor Viorel Barbu, Giuseppe Da Prato, Michael Röckner
en Limba Engleză Paperback – oct 2016
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.

The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".

The book will be of interest to PhD students and researchers in mathematics, physics and biology.
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Specificații

ISBN-13: 9783319410685
ISBN-10: 3319410687
Pagini: 204
Ilustrații: IX, 202 p.
Dimensiuni: 155 x 235 x 12 mm
Greutate: 0.31 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

Foreword.- Preface.- Introduction.- Equations with Lipschitz nonlinearities.- Equations with maximal monotone nonlinearities.- Variational approach to stochastic porous media equations.- L1-based approach to existence theory for stochastic porous media equations.- The stochastic porous media equations in Rd.- Transition semigroups and ergodicity of invariant measures.- Kolmogorov equations.- A Two analytical inequalities.- Bibliography.- Glossary.- Translator’s note.- Index.

Recenzii

“The authors of the monograph are renowned experts in the field of SPDEs and the book may be of interest not only to SPDE specialists but also to other researchers in mathematics, physics and biology.” (Bohdan Maslowski, Mathematical Reviews, July, 2018)

Textul de pe ultima copertă

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.

The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".

The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Caracteristici

This is the first book on stochastic porous media equations Concentrates on essential points, including existence, uniqueness, ergodicity and finite time extinction results Presents the state of the art of the subject in a concise, but reasonably self-contained way Includes both the slow and fast diffusion case, but also the critical case, modeling self-organized criticality