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Communications in Mathematical Physics

, Volume 136, Issue 3, pp 501–517 | Cite as

A kinetic equation with kinetic entropy functions for scalar conservation laws

  • Benoit Perthame
  • Eitan Tadmor
Article

Abstract

We construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws. In particular we prove that it is well-posed uniformly in ε — the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions — analogous to Boltzmann's microscopicH-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 ε↓0 to the unique entropy solution of the corresponding conservation law.

Keywords

Entropy Neural Network Nonlinear Dynamics Kinetic Equation Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Benoit Perthame
    • 1
  • Eitan Tadmor
    • 2
  1. 1.Départment de MathématiquesUniversité d'OrléansOrléans CX2France
  2. 2.School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael

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