On some problems concerning the nonlinear infiltration in unsaturated media

Abstract

The paper deals with the mathematical treatment of two specific models related to water infiltration in soils. The mathematical models consist of Richard’s equation with appropriate boundary and initial conditions. The hydraulic parameters (diffusivity, hydraulic conductivity, water capacity) that represent the coefficients of this equation are nonlinear functions. Depending on the situation studied, particularities that may arise are represented by the fact that the water capacity vanishes at the saturation value, implying that the equation degenerates at the interface between unsaturated-saturated flow and diffusivity blows up at the moisture saturation value in the unsaturated model. The paper develops a theory concerning the existence of the solution of each model apart.