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

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January 2009, 24(1): 35-57. doi: 10.3934/dcds.2009.24.35

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, Sweden
2.	Keldysh Institute of Applied Mathematics, Russian Academy of Science, Miusskaya Pl. 4, Moscow, 125047, Russian Federation

Received August 2007 Revised January 2008 Published January 2009

Abstract
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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.

Keywords: Lie group analysis., the Boltzmann equation, integral equations.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: A. V. Bobylev, Vladimir Dorodnitsyn. Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation. Discrete & Continuous Dynamical Systems - A, 2009, 24 (1) : 35-57. doi: 10.3934/dcds.2009.24.35

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