Shadow waves: Entropies and interactions for delta and singular shocks
type: Item
instance of: scholarly article
title: Shadow waves: Entropies and interactions for delta and singular shocks
zbMATH Open document ID: 1201.35134
author: Marko Nedeljkov
published in: Archive for Rational Mechanics and Analysis
publication date: 2010-09-10T00:00:00Z
review text: The author considers the conservation law \[ \partial_tf(U)+\partial_xg(U) = 0 \] with \(U:\mathbb R^2_+\rightarrow\mathbb R^n\), \(f,g:\mathbb R^n\rightarrow\mathbb R^n\). The focus is on the delta and singular shock solutions of the Riemann problem, their entropy admissibility conditions, and their interaction. The system is represented by piecewise constant functions called shadow waves. An example of three-dimensional pressureless gas dynamics is considered.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 5782731
zbMATH Keywords: conservation laws
zbMATH Keywords: shocks
zbMATH Keywords: shadow waves
zbMATH Keywords: Riemann problem
zbMATH Keywords: entropy admissibility conditions
zbMATH Keywords: three-dimensional pressureless gas dynamics
MaRDI profile type: Publication
full work available at URL: s00205-009-0281-2
OpenAlex ID: W1992222857
cites work: Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness
cites work: Sticky Particles and Scalar Conservation Laws
cites work: Hyperbolic systems of conservation laws
cites work: Formation of $\delta$-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Euler Equations for Isentropic Fluids
cites work: Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids
cites work: Q4409403
cites work: Q4701082
cites work: Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
cites work: Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics
cites work: Weak Solution to Pressureless Type System
cites work: Spaces of weighted measures for conservation laws with singular shock solutions
cites work: DELTA SHOCK WAVES AS A LIMIT OF SHOCK WAVES
cites work: Q4830166
cites work: Delta and singular delta locus for one-dimensional systems of conservation laws
cites work: Singular shock waves in interactions
cites work: Interactions of delta shock waves in a strictly hyperbolic system of conservation laws
cites work: On a representation of the prolonged systems for a scalar conservation law and on higher-order entropies
cites work: \(\delta ^{\prime }\)-shock waves as a new type of solutions to systems of conservation laws
cites work: Q4222728
cites work: The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach)
cites work: The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws
DOI: 10.1007/S00205-009-0281-2
description: scientific article; zbMATH DE number 5782731