Symmetries of evolution equations with non-localoperators and applications to the Boltzmann equation

A. V. Bobylev; Vladimir Dorodnitsyn

doi:10.3934/dcds.2009.24.35

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2009, Volume 24, Issue 1: 35-57. Doi: 10.3934/dcds.2009.24.35

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Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation

A. V. Bobylev^1, and
Vladimir Dorodnitsyn^2,

1.
Department of Mathematics, Karlstad University, SE-65188 Karlstad
2.
Keldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl. 4, Moscow, 125047

Received: August 2007

Revised: January 2008

Published: January 2009

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Abstract

In this paper we consider Lie group symmetries of evolution equations with non-local operators in context of applications to nonlinear kinetic equations. As an illustration we consider the Boltzmann equation and calculate the admitted group of point transformations.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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