Unilateral problems for nonlinear convection-reaction equations
type: Item
instance of: scholarly article
title: Unilateral problems for nonlinear convection-reaction equations
zbMATH Open document ID: 0861.35058
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1996-11-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73360
review text: The existence and uniqueness for a scalar conservation law related to Dirichlet's homogeneous boundary condition is established. More precisely for the problem \[ {\partial u\over\partial t}+\text{Div }f(U,t,x)+g(U,t,x)=0,\quad U\geq 0,\tag{1} \] two methods are developed: either a penalization of the equation (1) or an approximation procedure by parabolic problems whose diffusion term tends to zero. The model is a transcription, with some simplifications, of the mass conservation law of a chemical component and of the behaviour law. A motivation for this problem comes from the study of the two-phase creep of two fluids (oils and gases) in a porous medium in order to recover the hydrocarbons.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35L85
zbMATH DE Number: 942770
zbMATH Keywords: penalization
zbMATH Keywords: approximation procedure by parabolic problems
zbMATH Keywords: two-phase creep
author: Laurent Levi
reviewed by: Maria Agostina Vivaldi
MaRDI profile type: Publication
OpenAlex ID: W2333753372
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DOI: 10.5802/AFST.805
description: scientific article; zbMATH DE number 942770