Mathematical Models for Poroelastic Flows (Atlantis Studies in Differential Equations)

Meirmanov, Anvarbek

ISBN 10: 9462390142 / ISBN 13: 9789462390140

Published by Atlantis Press, 2013

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Seller Inventory # ERICA70494623901425

Bibliographic Details

• Title: Mathematical Models for Poroelastic Flows (Atlantis Studies in Differential Equations)
• Publisher: Atlantis Press
• Publication Date: 2013
• Language: English
• ISBN 10: 9462390142
• ISBN 13: 9789462390140
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.