Naslov
The unsaturated flow in porous media with dynamic capillary pressure

Autori
Milišić, Josipa-Pina

Izvornik
Journal of differential equations (0022-0396) 264 (2018), 9; 5629-5658

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
dynamic capillary pressure ; degenerate nonlinear parabolic PDE ; pseudoparabolic equations ; entropy ; existence of solutions

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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