No abstract

Filtration in porous media of fluids and gases containing associated with them (dissolved, particulate) solid substances is accompanied by the diffusion of these substances and mass transfer between the liquid (gas) and solid stages. The most common types of mass transfer are sorption and desorption, ion exchange, dissolution and crystallization, mudding, sulfation and suffusion, waxing. We consider the system of equations modeling the process of non-equilibrium sorption. We formulate a difference approximation of the differential problem by an implicit scheme. The solution to the difference problem is constructed by the sweep method. Basing on the numerical results, we can conclude the following: as the relaxation time decreases, the solution to the non-equilibrium problem tends to the solution of the equilibrium problem as the time increases.

A new model for liquid-solid phase transitions within the frame of complete NavierStokes equations in a liquid phase is proposed. It takes into account such properties of liquid as compressibility, viscosity, and heat conductivity. The local existence and uniqueness of a smooth solution to the related initial-boundary value problem is proved.Mathematics Subject Classification (1991). 35Q30, 76D05, 76N10, 80A22.

No abstract

In this article the global solvability of the initial-boundary value problems for the system of equations describing non-stationary flow of the viscous heat-conducting one-dimensional gas in time-decreasing non-rectangular domains is proved. (2000). Primary 35Q30; Secondary 76D05, 76N10. Mathematics Subject Classification