Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics system. I
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 26-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a linearized system of differential equations that approximately describes the dynamics of a viscous gas the problem of constructing for the given initial data the control boundary conditions of the first kind that accelerate the process of reaching the steady state solution is studied. The article provides a description of the algorithm and the estimate of rate of convergence in the differential case.
@article{VMUMM_2018_1_a3,
     author = {K. A. Zhukov and A. A. Kornev and A. V. Popov},
     title = {Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics {system.~I}},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--32},
     year = {2018},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a3/}
}
TY  - JOUR
AU  - K. A. Zhukov
AU  - A. A. Kornev
AU  - A. V. Popov
TI  - Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics system. I
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2018
SP  - 26
EP  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a3/
LA  - ru
ID  - VMUMM_2018_1_a3
ER  - 
%0 Journal Article
%A K. A. Zhukov
%A A. A. Kornev
%A A. V. Popov
%T Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics system. I
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2018
%P 26-32
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a3/
%G ru
%F VMUMM_2018_1_a3
K. A. Zhukov; A. A. Kornev; A. V. Popov. Acceleration of transition to stationary state for solutions to a linearized viscous gas dynamics system. I. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2018), pp. 26-32. http://geodesic.mathdoc.fr/item/VMUMM_2018_1_a3/

[1] Yanenko N.N., Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Izd-vo Novosib. gos. un-ta, Novosibirsk, 1966 | MR

[2] Vladimirova N.N., Kuznetsov B.G., Yanenko N.N., “Chislennyi raschet simmetrichnogo obtekaniya plastinki ploskim potokom vyazkoi neszhimaemoi zhidkosti”, Nekotorye voprosy vychislitelnoi i prikladnoi matematiki, Nauka, Novosibirsk, 1966, 29–35 | MR

[3] Temam R., “Une methode d'approkhimation de la solution des equations de Navier–Stokes”, Bull. Soc. math. France, 96 (1968), 115–152 | DOI | MR | Zbl

[4] Prohl A., Projection and quasi-compressibility methods for solving the incompressible Navier–Stokes equations, Stutgard, 1997 | MR

[5] Ransau S.R., Solution methods for incompressible viscous free surface flows: A Literature Review, Preprint No 3, Norwegian university of science and technology, Tronheim, Norway, 2002

[6] Shen J., “Pseudo-compressibility methods for the unsteady incompressible Navier–Stokes equations”, Proc. 1994 Beijing Symp. on Nonlinear Evolution Equations and Infinite Dynamical Systems, ed. Boling Guo, Zhong Shan University Press, 1997, 68–78 | MR

[7] Kobelkov G.M., “Simmetrichnye approksimatsii uravnenii Nave–Stoksa”, Matem. sb., 193:7 (2002), 87–108 | DOI | MR | Zbl

[8] Mikhailov V.P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[9] Zhukov K.A., Raznostnye i proektsionno-raznostnye skhemy dlya zadachi dvizheniya vyazkogo slaboszhimaemogo barotropnogo gaza, Kand. dis., M., 2008

[10] Fursikov A.V., “Stabiliziruemost kvazilineinogo parabolicheskogo uravneniya s pomoschyu granichnogo upravleniya s obratnoi svyazyu”, Matem. sb., 192:4 (2001), 115–160 | DOI | Zbl

[11] Fursikov A.V., “Stabilizability of two-dimensional Navier–Stokes equations with help of boundary feedback control”, J. Math. Fluid Mech., 3 (2001), 259–301 | DOI | MR | Zbl

[12] Fursikov A.V., “Realnye protsessy i realizuemost metoda stabilizatsii sistemy Nave–Stoksa posredstvom upravleniya s obratnoi svyazyu s granitsy oblasti”, Nelineinye zadachi matematicheskoi fiziki i smezhnye voprosy, V chest akademika O. A. Ladyzhenskoi, Mezhdunarodnaya matematicheskaya seriya, 2, Tamara Rozhkovskaya, Novosibirsk, 2002, 127–164 | MR

[13] Chizhonkov E.V., “Numerical aspects of one stabilization method”, Russ. J. Numer. Anal. Math. Modelling, 18:5 (2003), 363–376 | DOI | MR | Zbl

[14] Chizhonkov E.V., “Ob operatorakh proektirovaniya dlya chislennoi stabilizatsii”, Vychislitelnye metody i programmirovanie, 5 (2004), 161–169

[15] Vedernikova E.Yu., Kornev A.A., “K zadache o nagreve sterzhnya”, Vestn. Mosk. un-ta. Matem. Mekhan., 2014, no. 6, 10–15 | MR

[16] Kornev A.A., “Chislennoe modelirovanie protsessa asimptoticheskoi stabilizatsii po kraevym usloviyam kvazidvumernogo techeniya chetyrekhvikhrevoi struktury”, Matematicheskoe modelirovanie, 29:11 (2017), 99–110

[17] Kornev A.A., “The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type”, Russ. J. Numer. Anal. Math. Modelling, 32:4 (2017), 245–251 | DOI | MR | Zbl