A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves
type: Item
instance of: scholarly article
title: A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves
zbMATH Open document ID: 1041.35057
DOI: 10.1016/S0362-546X(02)00160-8
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The authors consider a vertical nonsteady groundwater flow with dynamic capillary pressure. The governing equation is of a diffusion-convection type, with a nonlinear third-order term. It is investigated a special case when the original problem reduces to a pseudo-parabolic Burgers equation \[ u_t= u_{xx}+ 2uu_x+ \varepsilon^2 u_{xxt}\quad\text{on }\mathbb{R}\times [0, T], \] with the initial condition \[ u(x)= u_0(x)\quad\text{in }\mathbb{R}, \] where \(\varepsilon> 0\) is a parameter. A well-posedness result for the initial value problem and the stability of travelling wave solutions are proved.
reviewed by: Ibrahim Aganović
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 1880004
zbMATH Keywords: unsaturated flow
zbMATH Keywords: dynamic capillary pressure
zbMATH Keywords: travelling waves
zbMATH Keywords: stability
author: C. M. Cuesta
author: Josephus Hulshof
MaRDI profile type: Publication
cites work: Mathematical model of the non equilibrium water oil displacement in porous strata
cites work: Theory of fluid flows through natural rocks
cites work: Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects
cites work: Q4748596
cites work: Infiltration in porous media with dynamic capillary pressure: travelling waves
cites work: Q3958836
cites work: The partial differential equation ut + uux = μxx
cites work: Analysis of a Darcy Flow Model with a Dynamic Pressure Saturation Relation
cites work: Behavior of the solutions of the Cauchy problem for certain quasilinear equations for unbounded increase of the time
cites work: Remarks on the Stability of Shock Profiles for Conservation Laws with Dissipation
cites work: Oscillatory instability of traveling waves for a KdV-Burgers equation
cites work: Differential models of hysteresis
full work available at URL: s0362-546x(02)00160-8
OpenAlex ID: W2001169386
description: scientific article; zbMATH DE number 1880004