Anvarbek Meirmanov - Böcker
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2 produkter
2 produkter
Del 1 - De Gruyter Series in Applied and Numerical Mathematics
Free Boundaries in Rock Mechanics
Inbunden, Engelska, 2017
1 703 kr
Skickas inom 5-8 vardagar
This monograph is concerned with free-boundary problems of partial differential equations arising in the physical sciences and in engineering. The existence and uniqueness of solutions to the Hele-Shaw problem are derived and techniques to deal with the Muskat problem are discussed. Based on these, mathematical models for the dynamics of cracks in underground rocks and in-situ leaching are developed. ContentsIntroductionThe Hele–Shaw problemA joint motion of two immiscible viscous fluidsMathematical models of in-situ leachingDynamics of cracks in rocksElements of continuum mechanics
Del 1 - Atlantis Studies in Differential Equations
Mathematical Models for Poroelastic Flows
Inbunden, Engelska, 2013
1 009 kr
Skickas inom 10-15 vardagar
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.