Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first-order equation on the boundary
The results of this paper can contribute to the prediction of the motion of pollutants applied at land surface. The authors use the model of saturation of porous medium in the case when lateral flow and infiltration are of comparable size. A weak solution is obtained by using known results on elliptic-parabolic equations and on boundary value problems for first-order quasilinear equations. The authors prove also the uniqueness and continuous dependence of solution on initial data in \(L^1\). Finally, the authors develop an asymptotic analysis for the layer with infiltration. Two small parameters are involved, related to the hydraulic conductivity and to the resistance of the layer.
boundary value problems for first-order quasilinear equations
continuous dependence of solution on initial data
scientific article; zbMATH DE number 1331012