Products of distributions, conservation laws and the propagation of \(\delta'\)-shock waves
type: Item
instance of: scholarly article
title: Products of distributions, conservation laws and the propagation of \(\delta'\)-shock waves
zbMATH Open document ID: 1288.46030
author: Carlos Orlando R. Sarrico
published in: Chinese Annals of Mathematics. Series B
publication date: 2012-12-06T00:00:00Z
review text: The paper first surveys a notion, proposed by the author, of product of certain distributions, then, with a definition of solution based on this distributional product, studies the propagation of singular travelling waves for conservation laws equations \(u_{t}+\left[ \phi (u)\right] _{x}=\psi (u),\)\ where \(\phi \)\ and \(\psi \)\ are entire functions. Conditions for\ the propagation of wave profiles \( \beta +m\delta \)\ and \(\beta +m\delta ^{\prime }\) are presented as well.
reviewed by: Chikh Bouzar
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6113068
zbMATH Keywords: conservations laws
zbMATH Keywords: travelling waves
zbMATH Keywords: \(\delta'\)-shock waves
zbMATH Keywords: \(\delta\)-shock waves
zbMATH Keywords: \(\delta\)-solitons
zbMATH Keywords: propagation of distributional wave profiles
MaRDI profile type: Publication
full work available at URL: s11401-012-0713-4
OpenAlex ID: W2108638635
cites work: Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness
cites work: Sticky Particles and Scalar Conservation Laws
cites work: Q3799227
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: Multiplications of distributions in elasticity and hydrodynamics
cites work: Definition and weak stability of nonconservative products
cites work: Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
cites work: Weak Solution to Pressureless Type System
cites work: Spaces of weighted measures for conservation laws with singular shock solutions
cites work: A study of numerical methods for hyperbolic conservation laws with stiff source terms
cites work: Traveling wave solutions of a nonlinear reaction-advection equation
cites work: A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction
cites work: Q4830166
cites work: Delta and singular delta locus for one-dimensional systems of conservation laws
cites work: Interactions of delta shock waves in a strictly hyperbolic system of conservation laws
cites work: Q3814225
cites work: Distributional products and global solutions for nonconservative inviscid Burgers equation
cites work: New solutions for the one-dimensional nonconservative inviscid Burgers equation
cites work: Collision of delta-waves in a turbulent model studied via a distribution product
cites work: Q3009373
cites work: Products of distributions and singular travelling waves as solutions of advection-reaction equations
DOI: 10.1007/S11401-012-0713-4
description: scientific article; zbMATH DE number 6113068