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


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.


Entropy Neural Network Nonlinear Dynamics Kinetic Equation Quantum Computing 
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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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