Analytic semigroup generated by the linearization of a Riemann-Dafermos solution
type: Item
instance of: scholarly article
title: Analytic semigroup generated by the linearization of a Riemann-Dafermos solution
zbMATH Open document ID: 1073.35160
author: Xiao-Biao Lin
published in: Dynamics of Partial Differential Equations
publication date: 2005-07-06T00:00:00Z
review text: The Riemann problem for the conservation law \(u_T + f(u)_X=0 \) is investigated. A Riemann-Dafermos solution is considered, i.e. a solution of Dafermos regularization \(u_T + f(u)_X=\varepsilon T u_{XX}\) that is close to a Riemann solution of the initial problem. In a self-similar coordinate \(x= \frac{X}{T}\) the Riemann-Dafermos solution becomes stationary. In the Banach space of bounded continuous functions with the appropriate weighted norm the linear variational system around such stationary solution is written in the form \(U_{\tau}=AU.\) The linear operator \(A\) is proved to be sectorial and hence \(A\) generates an analytic semigroup. Some important consequences of this result are discussed.
reviewed by: Elena V. Tabarintseva
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 2186759
zbMATH Keywords: Dafermos regularization
zbMATH Keywords: hyperbolic conservation law
zbMATH Keywords: Riemann-Dafermos
zbMATH Keywords: Riemann problem
MaRDI profile type: Publication
full work available at URL: dpde.2004.v1.n2.a2
OpenAlex ID: W2114496667
DOI: 10.4310/DPDE.2004.V1.N2.A2
description: scientific article; zbMATH DE number 2186759