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

Published online by Cambridge University Press:  21 October 2005

V. V. SHELUKHIN  and
C. I. KONDO
V. V. SHELUKHIN
Affiliation:
Lavrentyev Institute of Hydrodynamics, Lavrentyev pr. 15, Novosibirsk 630090, Russia email: shelukhin@hydro.nsc.ru
C. I. KONDO
Affiliation:
Federal University of Sao Carlos P. O. Box 676 13565-905, Sao Carlos-SP, Brazil e-mail: dcik@dm.ufscar.br
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Abstract

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.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 16 , Issue 4 , August 2005 , pp. 493 - 517
Copyright
2005 Cambridge University Press

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