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TMF, 2016, Volume 186, Number 2, Pages 221–229 (Mi tmf8884)  

This article is cited in 1 scientific paper (total 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

DOI: https://doi.org/10.4213/tmf8884

Full text: PDF file (387 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 186:2, 183–191

Bibliographic databases:

Received: 02.03.2015

Citation: O. V. Ilyin, “Symmetries and invariant solutions of the one-dimensional Boltzmann equation for inelastic collisions”, TMF, 186:2 (2016), 221–229; Theoret. and Math. Phys., 186:2 (2016), 183–191

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. R. Eftimie, “A few notions of stability and bifurcation theory”: R. Eftimie, Hyperbolic and Kinetic Models For Self-Organised Biological Aggregations: a Modelling and Pattern Formation Approach, Lect. Notes Math., Lecture Notes in Mathematics, 2232, Springer, 2018, 227–264  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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