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Stochastic porous media equations / Viorel Barbu, Giuseppe Da Prato and Michael Rockner.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics ; 2163.Publication details: Switzerland : Springer, 2016.Description: ix, 202 pages ; 24 cmISBN:
  • 9783319410685 (alk. paper)
Subject(s): DDC classification:
  • 519.23 23 B241
Contents:
1. Introduction -- 2. Equations with Lipschitz nonlinearities -- 3. Equations with maximal monotone nonlinearities -- 4. Variational approach to stochastic porous media equations -- 5. L1-based approach to existence theory for stochastic porous media equations -- 6. The stochastic porous media equations in Rd -- 7. Transition semigroup -- References -- Index.
Summary: 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 previously 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 519.23 B241 (Browse shelf(Opens below)) Available 137708
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Equations with Lipschitz nonlinearities --
3. Equations with maximal monotone nonlinearities --
4. Variational approach to stochastic porous media equations --
5. L1-based approach to existence theory for stochastic porous media equations --
6. The stochastic porous media equations in Rd --
7. Transition semigroup --
References --
Index.

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 previously 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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