Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Volume 22

Models of the Dynamics of Heterogeneous Media and the Body of Mathematics. Correctness ``In the Whole'' of the Boundary Problems for Equations of One-Dimensional Non-Stationary Motion of a Viscous Gas. Initial-Boundary Value Problems for the Navier-Stokes Equations of Nonhomogeneous Viscous Incompressible Fluid. Correctness of the Problem of Flow through an Ideal Incompressible Liquid. Filtration of Immiscible Liquids. References.

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations.

The investigations involve the results concerning Navier-Stokes equations of viscous heat-conductive gas, incompressible nonhomogeneous fluid and filtration of multi-phase mixture in a porous medium. The correctness of the initial boundary-value problems and the qualitative properties of solutions are also considered. The book is written for those who are interested in the theory of nonlinear partial differential equations and their applications in mechanics.