Geodesic
A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 482-493.

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

We obtain a priori estimates of the solution in the uniform metric for a linear conjugate initial-boundary inverse problem describing the joint motion of a binary mixture and a viscous heat-conducting liquid in a plane channel. With their help, it is established that the solution of the non-stationary problem with time growth tends to a stationary solution according to the exponential law when the temperature on the channel walls stabilizes with time.
Keywords: conjugate problem, inverse problem, a priori estimates, asymptotic behavior. 
@article{JSFU_2018_11_4_a9,
     author = {Victor K. Andreev and Marina V. Efimova},
     title = {A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {482--493},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a9/}
}
TY  - JOUR
AU  - Victor K. Andreev
AU  - Marina V. Efimova
TI  - A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 482
EP  - 493
VL  - 11
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a9/
LA  - en
ID  - JSFU_2018_11_4_a9
ER  - 
%0 Journal Article
%A Victor K. Andreev
%A Marina V. Efimova
%T A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 482-493
%V 11
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a9/
%G en
%F JSFU_2018_11_4_a9
Victor K. Andreev; Marina V. Efimova. A priori estimates of the adjoint problem describing the slow flow of a binary mixture and a fluid in a channel. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 482-493. http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a9/

[1] A. Nepomnyashii, I. Simanovskii, J.-C. Legros, Interfacial Convection in Multilayer System, Springer, New York, 2006 | MR

[2] R. Narayanan, D. Schwabe, Interfacial Fluid Dynamics and Transport Processes, Springer-Verlag, Berlin, 2003 | MR | Zbl

[3] R. Kh.Zeytovnian, Convection in Fluids, Springer, Dordrecht, 2009 | MR

[4] V. K. Andreev, V. E. Zakhvataev, E. A. Ryabitskii, Thermocapillary Instability, Nauka, Novosibirsk, 2000 (in Russian) | MR

[5] V.K. Andreev, “On Inequalities of the Friedrichs type for Combined Domains”, Journal Siberian Federal University. Mathematics and Physics, 2:2 (2009), 146–157 (in Russian)

[6] A. D. Polianin, Handbook of linear partial differential equations for engineers and scientists, Boca Raton, London, 2002 | MR

[7] M. V. Efimova, “On one two-dimensional stationary flow of a binary mixture and viscous fluid in a plane layer”, Journal Siberian Federal University. Mathematics and Physics, 9:1 (2016), 30–36 | DOI