Solvability of some inverse problems for the nonstationary heat-and-mass-transfer system

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• 作者：S.G. Pyatkov ; ^{pyatkov@math.nsc.ru" class="auth_mail" title="E-mail the corresponding author} ; M.L. Samkov ^{maxwell86@mail.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Parabolic equation ; Inverse problem ; Control problem ; Heat-and-mass transfer ; Navier&ndash ; Stokes system
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1449-1465
• 全文大小：456 K

文摘

We study solvability of inverse problems of finding the right-hand side together with a solution itself for the nonstationary heat-and-mass-transfer system. The system consists of the Navier–Stokes system whose right-hand side contains the temperature of a fluid and the concentration of an admixture and the parabolic equations for the temperature of a fluid and the concentration. The right-hand side of the equation for the concentration is unknown and characterizes the volumetric density of sources of an admixture in a fluid. The usual boundary conditions are supplemented with the overdetermination conditions which are the values of the concentration on some system of surfaces.