This article is cited in 1 paper

Symmetries and invariant solutions of the one-dimensional Boltzmann equation for inelastic collisions

O. V. Ilyin

Dorodnitsyn Computation Center, RAS, Moscow, Russia

Abstract: We consider the one-dimensional integro-differential Boltzmann equation for Maxwell particles with inelastic collisions. We show that the equation has a five-dimensional algebra of point symmetries for all dissipation parameter values and obtain an optimal system of one-dimensional subalgebras and classes of invariant solutions.

Keywords: inelastic Boltzmann equation, Lie symmetry, invariant solution, optimal system of subalgebras.

Received: 02.03.2015

DOI: 10.4213/tmf8884

 English version: Theoretical and Mathematical Physics, 2016, 186:2, 183–191

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