The Surface Evaporation Problem with Signorini Boundary Condition
Zhida Huang, Mario Primicerio · SIAM Journal on Mathematical Analysis · 1992
The one-dimensional filtration of an incompressible liquid in a homogeneous, isotropic, rigid porous medium is considered. The bottom of the layer is impermeable, whereas on the top surface a Signorini-type boundary condition is imposed. Existence and uniqueness of the weak solution are proved under general conditions. Then some qualitative properties of the solution and its asymptotic behaviour are analyzed. In particular, the characterization of the set $D \equiv \{ {t:u(0,t) = 0} \}$ is discussed.