03502nam 22006255 450 991030014540332120250717140312.09789462390157946239015010.2991/978-94-6239-015-7(OCoLC)869793335(MiFhGG)GVRL6XSU(CKB)3710000000075898(MiAaPQ)EBC1593342(MiFhGG)9789462390157(DE-He213)978-94-6239-015-7(EXLCZ)99371000000007589820131128d2014 u| 0engurun|---uuuuatxtccrMathematical Models for Poroelastic Flows /by Anvarbek Meirmanov1st ed. 2014.Paris :Atlantis Press :Imprint: Atlantis Press,2014.1 online resource (xxxviii, 449 pages) illustrations (some color)Atlantis Studies in Differential Equations,2214-6261 ;1"ISSN: 2214-6253."9789462390140 9462390142 Includes bibliographical references.Isothermal Liquid Filtration -- Filtration of a compressible thermo-fluid -- Hydraulic shock in incompressible poroelastic media -- Double porosity models for a liquid filtration -- Filtration in composite incompressible media -- Isothermal acoustics in poroelastic media -- Non-isothermal acoustics in poroelastic media -- Isothermal acoustics in composite media -- Double porosity models for acoustics -- Diffusion and convection in porous media -- The Muskat problem.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.Atlantis Studies in Differential Equations,2214-6261 ;1Differential equationsMathematical physicsMechanicsDifferential EquationsMathematical Methods in PhysicsClassical MechanicsDifferential equations.Mathematical physics.Mechanics.Differential Equations.Mathematical Methods in Physics.Classical Mechanics.515.353Meirmanov Anvarbekauthttp://id.loc.gov/vocabulary/relators/aut42636MiFhGGMiFhGGBOOK9910300145403321Mathematical Models for Poroelastic Flows2512355UNINA