Geodesic
Mathematical models of a diffusion-convection in porous media
Electronic journal of differential equations, Tome 2012 (2012)
Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.
Classification : 35B27, 46E35, 76R99
Keywords: diffusion-convection, liquid filtration, homogenization 
@article{EJDE_2012__2012__a89,
     author = {Meirmanov,  Anvarbek M. and Zimin,  Reshat},
     title = {Mathematical models of a diffusion-convection in porous media},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1253.35124},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a89/}
}
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Meirmanov,  Anvarbek M.; Zimin,  Reshat. Mathematical models of a diffusion-convection in porous media. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a89/