Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables

1998 ◽  
Vol 92 (6) ◽  
pp. 4231-4255
Author(s):  
A. A. Arkhipova
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Systems ◽  
Global Solvability ◽  
Spatial Variables ◽  
Variational Structure

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.

On parabolic systems with variational structure

1985 ◽  
Vol 54 (1-2) ◽  
pp. 53-82 ◽  
Author(s):  
Wilfried Wieser
Keyword(s):  
Parabolic Systems ◽  
Variational Structure
Sign in / Sign up

Export Citation Format

Share Document