A Kinetic Equation with Kinetic Entropy Functions for Scalar Conservation Laws

Abstract

We construct a nonlinear kinetic equation and prove that it is well- adapted to describe general multidimensional scalar conservation laws. In particular we prove that it is well-posed uniformly in epsilon - the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, we prove by both - BV compactness arguments in the multidimensional case and by compensated compactness arguments in the one- dimensional case, that the local density of kinetic particles admits a 'continuum' limit, as it converges strongly with epsilon down to 0 to the unique entropy solution of the corresponding conversation law. (Author) (kr)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA227103

Entities

People

  • Benoit Perthame
  • Eitan Tadmor

Tags

DTIC Thesaurus Topics

  • Aeronautics
  • Applied Mathematics
  • Boltzmann Equation
  • Computers
  • Contracts
  • Convergence
  • Engineering
  • Equations
  • Euler Equations
  • Inequalities
  • Mathematics
  • Nonlinear Analysis
  • Particles
  • Scalar Functions
  • Shock Waves
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Explosive Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.