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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

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 and Continuous Dynamical Systems, 2009, 24 (1) : 35-57. doi: 10.3934/dcds.2009.24.35
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