A degenerate hydrodynamic dispersion model | [Journal of Prime Research in Mathematics • 2007]

Author(s):

1. SERGEY SAZHENKOV: Lavrentyev Institute of Hydrodynamics, Novosibirsk 630090, Russia.

Abstract:

A Cauchy problem for a two-dimensional ultra-parabolic model of filtration through a porous ground of a viscous incompressible fluid containing a solute (tracer) is considered. The °uid is driven by the buoyancy force. The phenomenon of molecular diffusion of the tracer into the porous ground is taken into account. The porous ground consists of one-dimensional filaments oriented along some smooth non-degenerate vector field. Two cases are distinguished depending on spatial orientation of the ¯laments, and existence of generalized entropy solutions is proved for the both. In the first case, all filaments are parallel to the buoyancy (gravitational) force and, except for this, the equations of the model have rather general forms. In the second case, the filaments can be nonparallel to the buoyancy force and to each other, in general, but their geometric structure must be genuinely nonlinear. The proofs rely on the method of kinetic equation and the theory of Young measures and H-measures.

Page(s): 140-153

DOI: DOI not available

Published: Journal: Journal of Prime Research in Mathematics, Volume: 3, Issue: 1, Year: 2007

Keywords:

AMS SUBJECT , 76S05 , 76R50 , NonIsotropic Porous Medium , 35K65 , Nonlinear Di®usionConvection , 35D05 , Genuine Nonlinearity , Ultraparabolic Equation

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