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

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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. 
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     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/}
}
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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/