Seminar in the framework of the PDE Afternoon



19.12.2017
Type seminar
Time 15:00 - 15:45
Place Vienna University of Technology, Wiedner Hauptstraße 8, Vienna (map)
Room Seminarraum DA Grün 03B
Speaker Josipa-Pina Milišić (University of Zagreb, Croatia)
Title The unsaturated flow in porous media with dynamic capillary pressure
Abstract In this talk 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. 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, we will show how to obtain an estimate of the mixed-derivative term by combining the information from the capillary pressure with obtained a priori estimates on the saturation.