Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
type: Item
instance of: scholarly article
title: Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
zbMATH Open document ID: 1072.35121
published in: Journal of Differential Equations
publication date: 2005-05-04T00:00:00Z
review text: The authors consider the system of conservation laws \[ u_t+(F(u,v))_x=0, \quad v_t+(G(u,v))_x=0, \] where the real functions \(F(u,v)\) and \(G(u,v)\) are smooth with respect to their arguments and linear in \(v\). Here \(u=u(x,t)\in \mathbb R \) and \(v=v(x,t)\in \mathbb R \) are unknown functions which depend on real arguments. A new definition of a \(\delta \)-shock wave type solution for the system under consideration is introduced. The authors establish a new weak asymptotics method by which they construct formulas describing the propagation and interaction of \(\delta \)-shock waves. The merging of two \(\delta \)-shock waves is discussed as well.
reviewed by: Dimitar A. Kolev
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 2164779
zbMATH Keywords: weak asymptotics method
zbMATH Keywords: merging of two \(\delta \)-shock waves
author: V. G. Danilov
author: V. M. Shelkovich
MaRDI profile type: Publication
full work available at URL: j.jde.2004.12.011
OpenAlex ID: W1984699983
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DOI: 10.1016/J.JDE.2004.12.011
description: scientific article; zbMATH DE number 2164779