The joint creeping motion of three viscid liquids in a plane layer: A priori estimates and convergence to steady flow

Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.1134/S1990478916010026

Ключевые слова: a priori estimates, asymptotic behavior, conjugate initial-boundary value problem, thermocapillarity, Boundary value problems, Estimation, Heat conduction, Initial value problems, Liquids, Nonlinear equations, A-priori estimates, Asymptotic behaviors, Conducting liquid, Immiscible liquids, Initial-boundary value problems, Invariant solutions, Non-linear inverse problem, Thermocapillarity, Inverse problems

Аннотация: We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes. © 2016, Pleiades Publishing, Ltd.

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Издание

Журнал: Journal of Applied and Industrial Mathematics

Выпуск журнала: Vol. 10, Is. 1

Номера страниц: 7-20

ISSN журнала: 19904789

Авторы

  • Andreev V.K. (Siberian Federal University)
  • Cheremnykh N. (Siberian Federal University)

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