A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws
type: Item
instance of: scholarly article
title: A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws
zbMATH Open document ID: 0911.35073
author: Roberto Natalini
published in: Journal of Differential Equations
publication date: 1998-10-21T00:00:00Z
review text: We present a new relaxation approximation to scalar conservation laws in several space variables by means of semilinear hyperbolic systems of equations with a finite number of velocities. Under a suitable multidimensional generalization of the Whitham relaxation subcharacteristic condition, we show the convergence of the approximated solutions to the unique entropy solution of the equilibrium Cauchy problem.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 1213738
zbMATH Keywords: Chapman-Enskop analysis
zbMATH Keywords: Maxwellian functions
zbMATH Keywords: relaxation approximation
zbMATH Keywords: Whitham relaxation subcharacteristic condition
Wikidata QID: Q57777049
MaRDI profile type: Publication
OpenAlex ID: W1981857852
cites work: Q4370484
cites work: Q4247498
cites work: Résolution d'équations d'évolution quasilinéaires en dimension N d'espace à l'aide d'équations linéaires en dimension \(N+1\)
cites work: A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
cites work: The fluid-dynamical limit of a nonlinear model boltzmann equation
cites work: The Boltzmann equation and its applications
cites work: The mathematical theory of dilute gases
cites work: Zero relaxation and dissipation limits for hyperbolic conservation laws
cites work: Hyperbolic conservation laws with stiff relaxation terms and entropy
cites work: Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography
cites work: Numerical Passage from Kinetic to Fluid Equations
cites work: Q4189096
cites work: A kinetic construction of global solutions of first order quasilinear equations
cites work: Numerical approximation of hyperbolic systems of conservation laws
cites work: Weakly coupled systems of quasilinear boundary value problem with applications to semilinear elliptic equations
cites work: Convergence Results for Some Conservation Laws with a Reflux Boundary Condition and a Relaxation Term Arising in Chemical Engineering
cites work: Kinetic formulation for chromatography and some other hyperbolic systems
cites work: A convex entropy for a hyperbolic system with relaxation
cites work: The relaxation schemes for systems of conservation laws in arbitrary space dimensions
cites work: Contractive relaxation systems and the scalar multidimensional conservation law
cites work: Q5601102
cites work: A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations
cites work: Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
cites work: Q4884695
cites work: Hyperbolic conservation laws with relaxation
cites work: BV solutions and relaxation limit for a model in viscoelasticity
cites work: \(L^ 1\) nonlinear stability of traveling waves for a hyperbolic system with relaxation
cites work: Q4892756
cites work: Global existence to the BGK model of Boltzmann equation
cites work: Boltzmann Type Schemes for Gas Dynamics and the Entropy Property
cites work: Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions
cites work: A kinetic equation with kinetic entropy functions for scalar conservation laws
cites work: Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory
cites work: Q5533735
cites work: Systems of Ordinary Differential Equations Which Generate an Order Preserving Flow. A Survey of Results
cites work: On the Rate of Convergence to Equilibrium for a System of Conservation Laws with a Relaxation Term
cites work: Asymptotic limit of initial boundary value problems for conservation laws with relaxational extensions
cites work: Q4151274
cites work: The fluid-dynamic limit of the Broadwell model of the nonlinear Boltzmann equation in the presence of shocks
DOI: 10.1006/JDEQ.1998.3460
description: scientific article; zbMATH DE number 1213738