Analysis of a new model for unsaturated flow in porous media including hysteresis and dynamic effects (Q1598867)

The authors propose a model for unsaturated flows in porous media. This takes into account simple play-type hysteresis and a dynamic term in the capillary equation. Existence and uniqueness of solutions are investigated, and qualitative properties of solutions are analyzed. For numerical computation the governing equation is recast into an elliptic problem for fluid pressure and an evolution equation for water content. The paper confines to the analysis of nondegenerate solutions only. Numerical results are compared with results available in the literature. However, an experimental validation is required to verify the new model.