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arXiv · 1703.10662

The unsaturated flow in porous media with dynamic capillary pressure

Josipa-Pina Milišić
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Abstract

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 in [12] 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 obtained a priori estimates on the saturation.

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Josipa-Pina Milišić. 2018-01-03. The unsaturated flow in porous media with dynamic capillary pressure. https://arxiv.org/abs/1703.10662

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