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Article information
2002 , Volume 7, ¹ 2, p.35-49
Grigoryev Y.N., Meleshko S.V.
Group analysis of integrodifferential kinetic equations. Results and perspective
The paper contains a survey of original authors studies on group theory analysis of integrodifferential kinetic equations of Boltzmann, Smolukhovsiy, Vlasov and others. Scheme of direct method for calculation of widest Lie groups (algebras) admitted by these equations is given. The groups, optimal systems of their subgroups and new invariant solutions obtained by authors for concrete equations are considered.
[full text] Classificator Msc2000:- *45K05 Integro-partial differential equations
- 58D19 Group actions and symmetry properties
- 76P05 Rarefied gas flows, Boltzmann equation
- 58J70 Invariance and symmetry properties
- 82C40 Kinetic theory of gases
Keywords: integro-differential kinetic equations, Boltzmann equation, Smolukhovskij equation, Vlasov equation, group classification, group invariant solutions, optimal system, Lie point symmetries, Lie algebras, asymptotic collision integral, Lie groups, Fourier transform
Author(s):
Grigoryev Yurii Nikolaevich
Dr. , Professor
Position: General Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Phone Office: (383) 330 87 45
E-mail: grigor@ict.nsc.ru
Meleshko S V
Office: ITAM SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Bibliography link:
Grigoryev Y.N., Meleshko S.V. Group analysis of integrodifferential kinetic equations. Results and perspective // Computational technologies. 2002. V. 7. ¹ 2. P. 35-49
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