The unsaturated flow in porous media with dynamic capillary pressure (CROSBI ID 248544)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Milišić, Josipa-Pina
engleski
The unsaturated flow in porous media with dynamic capillary pressure
In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure- saturation relationship where the relaxation parameter depends on the saturation. Following the approach given by Mikelić in [13] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed-derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation.
dynamic capillary pressure ; degenerate nonlinear parabolic PDE ; pseudoparabolic equations ; entropy ; existence of solutions
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Podaci o izdanju
264 (9)
2018.
5629-5658
objavljeno
0022-0396
1090-2732
10.1016/j.jde.2018.01.014