Geodesic
Symmetries of a class of quasilinear pseudoparabolic equations. Invariant solutions
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 90-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A qusilinear pseudoparabolic type equation with a free element depending on the second derivative with respect to the spatial variable is researched by the methods of the group analysis. Four-dimensional kernel of principal groups of the equation and specifications of the free element leading to fifth symmetries are found. Optimal systems of one-dimensional subalgebras of the principal Lie algebras for the equations and some invariant solutions are calculated.
Keywords: symmetries group of differential equation, group analysis, Lie algebra
Mots-clés : optimal system of subalgebras, invariant solution. 
@article{VCHGU_2012_15_a6,
     author = {V. E. Fedorov and A. V. Panov and A. S. Karabaeva},
     title = {Symmetries of a class of quasilinear pseudoparabolic equations. {Invariant} solutions},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {90--111},
     year = {2012},
     number = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a6/}
}
TY  - JOUR
AU  - V. E. Fedorov
AU  - A. V. Panov
AU  - A. S. Karabaeva
TI  - Symmetries of a class of quasilinear pseudoparabolic equations. Invariant solutions
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2012
SP  - 90
EP  - 111
IS  - 15
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a6/
LA  - ru
ID  - VCHGU_2012_15_a6
ER  - 
%0 Journal Article
%A V. E. Fedorov
%A A. V. Panov
%A A. S. Karabaeva
%T Symmetries of a class of quasilinear pseudoparabolic equations. Invariant solutions
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2012
%P 90-111
%N 15
%U http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a6/
%G ru
%F VCHGU_2012_15_a6
V. E. Fedorov; A. V. Panov; A. S. Karabaeva. Symmetries of a class of quasilinear pseudoparabolic equations. Invariant solutions. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 90-111. http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a6/

[1] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978, 400 pp. | MR

[2] N. Kh. Ibragimov, Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983, 280 pp. | MR

[3] N. H. Ibragimov, Selected Works, v. 1,2, Alga Publications, Blekinge Institute of Technology, Karlskrona, Sweden, 2001

[4] V. I. Lagno, C. V. Spichak, V. I. Stognii, Simmetriinyi analiz uravnenii evolyutsionnogo tipa, In-t kompyuter. issled., M.–Izhevsk, 2004, 392 pp.

[5] V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachev, A. A. Rodionov, Primenenie teoretiko-gruppovykh metodov v gidrodinamike, Nauka, Novosibirsk, 1994 | MR

[6] Y. N. Grigoriev, N. H. Ibragimov, V. F. Kovalev, S. V. Meleshko, Symmetries of Integro-Differential Equations: With Applications in Mechanics and Plasma Physics, Springer, Dordrecht, 2010 | MR | Zbl

[7] Yu. A. Chirkunov, S. V. Khabirov, Elementy simmetriinogo analiza differentsialnykh uravnenii mekhaniki sploshnoi sredy, NGTU, Novosibirsk, 2011, 659 pp.

[8] G. V. Demidenko, S. V. Uspenskii, Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauch. kn., Novosibirsk, 1998, 438+xviii pp. | MR

[9] A. G. Sveshnikov, A. B. Alshin, M. O. Korpusov, Yu. D. Pletner, Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007, 736 pp.

[10] G. I. Barenblatt, Yu. P. Zheltov, I. N. Kochina, “Ob osnovnykh predstavleniyakh teorii filtratsii odnorodnykh zhidkostei v treschinovatykh porodakh”, Priklad. matematika i mekhanika, 24:5 (1960), 852–864 | Zbl

[11] L. V. Ovsyannikov, “Programma «Podmodeli». Gazovaya dinamika”, Priklad. matematika i mekhanika, 58:4 (1994), 30–55 | MR | Zbl

[12] N. Kh. Ibragimov, Prakticheskii kurs differentsialnykh uravnenii i matematicheskogo modelirovaniya, Izd-vo Nizhegorod. un-ta im. N. I. Lobachevskogo, N. Novgorod, 2007, 421 pp.