scholarly journals On the existence of global solution of the system of equations of liquid movement in porous medium

2021 ◽  
Vol 234 ◽  
pp. 00095
Author(s):  
Margarita Tokareva ◽  
Alexander Papin
Keyword(s):  
Porous Medium ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Solvability ◽  
Compressible Liquid ◽  
Fluid Filtration ◽  
One Dimensional ◽  
Lagrangian Variables ◽  
Initial Boundary Value ◽  
Liquid Movement

The initial-boundary value problem for the system of one-dimensional isothermal motion of viscous liquid in deformable viscous porous medium is considered. Local theorem of existence and uniqueness of problem is proved in case of compressible liquid. In case of incompressible liquid the theorem of global solvability in time is proved in Holder classes. A feature of the model of fluid filtration in a porous medium considered in this paper is the inclusion of the mobility of the solid skeleton and its poroelastiс properties. The transition from Euler variables to Lagrangian variables is used in the proof of the theorems.

scholarly journals Filtration of Liquid in a Non-isothermal Viscous Porous Medium

2020 ◽  
pp. 763-773
Author(s):  
Alexander A. Papin ◽  
Margarita A. Tokareva ◽  
Rudolf A. Virts
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
System Of Equations ◽  
One Dimensional ◽  
Unsteady Fluid ◽  
Initial Boundary Value

The solvability of the initial-boundary value problem is proved for the system of equations of one-dimensional unsteady fluid motion in a heat-conducting viscous porous medium

scholarly journals On the Solutions of a Porous Medium Equation with Exponent Variable

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Huashui Zhan
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Boundary Value ◽  
Porous Medium Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Medium Equation ◽  
Special Cases ◽  
The Stability ◽  
Initial Boundary Value

The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.

A Mixture Theory for Quasi-One-Dimensional Diffusion in Fiber-Reinforced Composites

1978 ◽  
Vol 100 (1) ◽  
pp. 128-133 ◽  
Author(s):  
A. Maewal ◽  
G. A. Gurtman ◽  
G. A. Hegemier
Keyword(s):  
Mixture Theory ◽  
Moisture Diffusion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fiber Direction ◽  
One Dimensional ◽  
Transient Solutions ◽  
Initial Boundary Value ◽  
Direction Model ◽  
Diffusion Problems

A binary mixture theory is developed for heat transfer in unidirectional fibrous composites with periodic, hexagonal microstructure. The case treated concerns a class of problems for which heat conduction occurs primarily in the fiber direction. Model construction is based upon an asymptotic technique wherein the ratio of transverse-to-longitudinal thermal diffusion times is assumed to be small. The resulting theory contains information on the distribution of temperature and heat flux in individual components. Mixture accuracy is estimated by comparing transient solutions of the mixture equations with finite difference solutions of the Diffusion Equation for an initial boundary value problem. Excellent correlation between “exact” and mixture solutions is observed. The construction procedures utilized herein are immediately applicable to other diffusion problems—in particular, moisture diffusion.

Non-local parabolic systems: applications in the three-phase capillary fluid filtration

2005 ◽  
Vol 16 (4) ◽  
pp. 493-517 ◽  
Author(s):  
V. V. SHELUKHIN ◽  
C. I. KONDO
Keyword(s):  
Parabolic Systems ◽  
Initial Boundary ◽  
Pressure Control ◽  
Global Solvability ◽  
Fluid Filtration ◽  
Three Phase ◽  
Non Local ◽  
Degenerate Parabolic ◽  
Initial Boundary Value ◽  
Diffusion Tensors

Non-local degenerate parabolic systems arise in three-phase capillary flows in porous media under a pressure control at the inflow- and outflow-boundaries. A mathematical study of such systems is performed for a class of capillarity pressure functions corresponding to triangular capillarity-diffusion tensors. To this end a theory of non-degenerate parabolic approximations is developed: the unique global solvability of initial boundary-value problems is proved.

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