Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first-order equation on the boundary
type: Item
instance of: scholarly article
title: Modelling surface runoff and infiltration of rain by an elliptic-parabolic equation coupled with a first-order equation on the boundary
zbMATH Open document ID: 0963.76086
author: Ján Filo
author: Stephan Luckhaus
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-06-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76M45
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 1331012
zbMATH Keywords: existence
zbMATH Keywords: two small parameters
zbMATH Keywords: pollutants
zbMATH Keywords: saturation of porous medium
zbMATH Keywords: lateral flow
zbMATH Keywords: infiltration
zbMATH Keywords: weak solution
zbMATH Keywords: elliptic-parabolic equations
zbMATH Keywords: boundary value problems for first-order quasilinear equations
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence of solution on initial data
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: hydraulic conductivity
zbMATH Keywords: resistance
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: s002050050140
OpenAlex ID: W2057987041
DOI: 10.1007/S002050050140
description: scientific article; zbMATH DE number 1331012