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

Marinoschi, Gabriela

Differ. Integral Equ. 16, No. 9, 1093-1110 (2003).

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.

MSC:

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