KRM
On some properties of linear and linearized Boltzmann collision operators for hard spheres
A. V. Bobylev E. Mossberg
Kinetic & Related Models 2008, 1(4): 521-555 doi: 10.3934/krm.2008.1.521
The linear and the linearized Boltzmann collision operators for hard spheres are studied by a method based on reduction of integral equations to differential equations. We use this approach (in combination with numerical methods) to study the eigenvalues of the operators. We also use the differential equations to investigate large energy asymptotics of solutions to linear integral equations related to the Chapman-Enskog expansion.
keywords: Boltzmann equation hard spheres model eigenvalues
DCDS
Symmetries of evolution equations with non-local operators and applications to the Boltzmann equation
A. V. Bobylev Vladimir Dorodnitsyn
Discrete & Continuous Dynamical Systems - A 2009, 24(1): 35-57 doi: 10.3934/dcds.2009.24.35
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

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