Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes
type: Item
instance of: scholarly article
title: Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes
zbMATH Open document ID: 1246.35125
author: Nicolas Seguin
author: Boris Andreianov
published in: Discrete and Continuous Dynamical Systems
publication date: 2012-05-30T00:00:00Z
review text: The authors define entropy weak solutions and establish well-posedness for the Cauchy problem for the Burgers equation with a resonant singular source term. The interpretation of the non-conservative product in the source term follows the analysis of \textit{F. Lagoutière, N. Seguin} and \textit{T. Takahashi} [J. Differ. Equations 245, No. 11, 3503--3544 (2008; Zbl 1151.76033)]. For proving existence and for practical computation of solutions, the authors construct a finite volume scheme, which turns out to be a well-balanced scheme and which allows a simple and efficient treatment of the interface coupling. Numerical illustrations are given.
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 6039430
zbMATH Keywords: fluid-particle interaction
zbMATH Keywords: non-conservative coupling
zbMATH Keywords: well-posedness
zbMATH Keywords: interface traces
zbMATH Keywords: adapted entropies
zbMATH Keywords: finite volume scheme
reviewed by: Qin Meng Zhao
MaRDI profile type: Publication
full work available at URL: dcds.2012.32.1939
OpenAlex ID: W2330783814
DOI: 10.3934/DCDS.2012.32.1939
description: scientific article; zbMATH DE number 6039430