Stochastic Porous Media Equations

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 202 S.
ISBN-13:	9783319410685
ISBN-10:	3319410687
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Barbu, Viorel Röckner, Michael Da Prato, Giuseppe
Auflage:	1st edition 2016
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 12 mm
Von/Mit:	Viorel Barbu (u. a.)
Erscheinungsdatum:	01.10.2016
Gewicht:	0,335 kg