A Priori Estimates of the Adjoint Problem Describing the Slow Flow of a Binary Mixture and a Fluid in a Channel
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https://elib.sfu-kras.ru/handle/2311/71746Author:
Andreev, Victor K.
Efimova, Marina V.
Андреев, Виктор К.
Ефимова, Марина В.
Date:
2018-08Journal Name:
Журнал Сибирского федерального университета. Математика и физика. Journal of Siberian Federal University. Mathematics & Physics;2018 11 (4)Abstract:
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 Для линейной сопряженной начально-краевой обратной задачи, описывающей совместное движение бинарной смеси и вязкой теплопроводной жидкости в плоском канале, получены априорные
оценки решения в равномерной метрике. С их помощью установлено, что решение нестационарной задачи с ростом времени стремится к стационарному решению по экспоненциальному
закону, если температура на стенках канала стабилизируется со временем
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