Kinetic Equations and Hyperbolic Systems of Conversation Laws

Benoît Perthame
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Benoît Perthame: Université Pierre et Marie Curie, Laboratoire d’Analyse Numérique

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1118-1125 from Springer

Abstract: Abstract We present several recent results concerning the global existence of solutions to kinetic equations, which are, generally, semi-linear or quasi-linear hyperbolic partial differential equations of transport type. The most famous of them are certainly the Boltzmann or Vlasov-Poisson equations. We describe more precisely some general tools that can be used for their analysis: compactness results and dispersive effects. Then we give a new point of view on their fluid limits. This allows us to recover some nonlinear hyperbolic systems of conservation laws by a singular perturbation according to the “mean free path”.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_104

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