BV estimates for multicomponent chromatography with relaxation
type: Item
instance of: scholarly article
title: BV estimates for multicomponent chromatography with relaxation
zbMATH Open document ID: 1018.35052
author: Alberto Bressan
author: Wen Shen
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors consider the system of \(2n\) balance laws \[ \begin{cases} u_t+u_x=- {1\over\varepsilon} \bigl(F(u)-v\bigr),\\ v_t= {1\over\varepsilon} \bigl(F(u)- v\bigr) \end{cases}\tag{1} \] with initial data \(u(0,x)=u_0(x)\), \(v(0,x) = v_0(x)\). This system arises from the modelling of multicomponent chromatography. Letting the relaxation parameter \(\varepsilon\to 0\), one expects that the solution to (1) converges to \[ \begin{cases} \bigl(u+F(u) \bigr)_t+ u_x=0,\\ v=F(u).\end{cases} \] The goal of the authors is to provide a rigorous proof of this convergence, valid for all solutions with small total variation. To realize this program they use in particular probabilistic arguments.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 1492624
zbMATH Keywords: probabilistic approach
zbMATH Keywords: multicomponent chromatography
zbMATH Keywords: solutions with small total variation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.2000.6.21
OpenAlex ID: W2016319720
DOI: 10.3934/DCDS.2000.6.21
description: scientific article; zbMATH DE number 1492624