Geodesic
Mathematical and сomputer modeling of nonlinear waves dynamics in a coaxial physically nonlinear shells with viscous incompressible fluid between them
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 96-104 
A. Yu. Blinkova; A. D. Kovalev; I. A. Kovaleva; L. I. Mogilevich. Mathematical and сomputer modeling of nonlinear waves dynamics in a coaxial physically nonlinear shells with viscous incompressible fluid between them. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 96-104. http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a14/
@article{ISU_2012_12_3_a14,
     author = {A. Yu. Blinkova and A. D. Kovalev and I. A. Kovaleva and L. I. Mogilevich},
     title = {Mathematical and {\cyrs}omputer modeling of nonlinear waves dynamics in a~coaxial physically nonlinear shells with viscous incompressible fluid between them},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {96--104},
     year = {2012},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a14/}
}
TY  - JOUR
AU  - A. Yu. Blinkova
AU  - A. D. Kovalev
AU  - I. A. Kovaleva
AU  - L. I. Mogilevich
TI  - Mathematical and сomputer modeling of nonlinear waves dynamics in a coaxial physically nonlinear shells with viscous incompressible fluid between them
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2012
SP  - 96
EP  - 104
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a14/
LA  - ru
ID  - ISU_2012_12_3_a14
ER  - 
%0 Journal Article
%A A. Yu. Blinkova
%A A. D. Kovalev
%A I. A. Kovaleva
%A L. I. Mogilevich
%T Mathematical and сomputer modeling of nonlinear waves dynamics in a coaxial physically nonlinear shells with viscous incompressible fluid between them
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2012
%P 96-104
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a14/
%G ru
%F ISU_2012_12_3_a14

Voir la notice de l'article provenant de la source Math-Net.Ru

This study focuses on the analysis of nonlinear wave propagation deformations in the elastic physically nonlinear coaxial cylindrical shells containing a viscous incompressible fluid between them. Wave processes in an elastic cylindrical shell without interacting with fluid were previously studied from the standpoint of the theory of solitons. The presence of fluid required developing a new mathematical model and computer modeling of processes occurring in the system.

[1] B. Buchberger, F. Winkler (eds.), Gröbner Bases and Applications, London Mathematical Society Lectures Notes. Ser., 251, Cambridge University Press, 1998, 522 pp. | MR

[2] Gerdt V. P., Blinkov Yu. A., Mozzhilkin V. V., “Gröbner bases and generation of difference schemes for partial differential equations”, Symmetry, Integrability and Geometry: Methods and Applications, 2 (2006), 051, 26 pp. ; (дата обращения 28.02.10) URL: http://www.emis.de/journals/SIGMA/2006/Paper051/index.html | MR | Zbl

[3] Zemlyanukhin A. I., Mogilevich L. I., “Nelineinye volny deformatsii v tsilindricheskikh obolochkakh”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 3:1 (1995), 52–58

[4] Zemlyanukhin A. I., Mogilevich L. I., Nelineinye volny v tsilindricheskikh obolochkakh: solitony, simmetrii, evolyutsiya, Sarat. gos. tekhn. un-t, Saratov, 1999, 132 pp.

[5] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Drofa, M., 2003, 840 pp.

[6] Kauzerer K., Nelineinaya mekhanika, Izd-vo inostr. lit., M., 1961, 240 pp. | MR

[7] Volmir A. S., Obolochki v potoke zhidkosti i gaza: zadachi gidrouprugosti, Nauka, M., 1979, 320 pp.

[8] Maxima, a Computer Algebra System, URL: , (data obrascheniya 28.02.10) http://maxima.sourceforge.net/

[9] Blinkov Yu. A., Gerdt V. P., “Spetsializirovannaya sistema kompyuternoi algebry GINV”, Programmirovanie, 34:2 (2008), 67–80 | MR | Zbl

[10] Blinkov Yu. A., Mozzhilkin V. V., “Generatsiya raznostnykh skhem dlya uravneniya Byurgersa postroeniem bazisov Grëbnera”, Programmirovanie, 32:2 (2006), 71–74 | MR | Zbl

[11] SciPy.org, URL: , (data obrascheniya 28.02.10) http://www.scipy.org