Nonlinear infiltration with a singular diffusion coefficient. (English) Zbl 1161.76583

Summary: This paper deals with the study of the nonlinear boundary-value problem with initial data, modelling incompressible water infiltration into a homogeneous, isotropic, unsaturated soil, for nonhomogeneous Dirichlet boundary conditions. For some well-known hydraulic models, Richards’ equation that describes the evolution of the volumetric water content has the particularity that the diffusion coefficient blows up at a certain value of the soil moisture. In this paper, for a problem of this type, a result of existence and uniqueness of the solution is proved for the unsaturated flow, and its properties are deduced. Conditions under which saturation occurrence is possible are finally discussed.


76S05 Flows in porous media; filtration; seepage
35K57 Reaction-diffusion equations
47N20 Applications of operator theory to differential and integral equations