Geodesic
Coefficient inverse extremum problems for stationary heat and mass transfer equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1055-1076

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A technique is developed for analyzing coefficient inverse extremum problems for a stationary model of heat and mass transfer. The model consists of the Navier-Stokes equations and the convection-diffusion equations for temperature and the pollutant concentration that are nonlinearly related via buoyancy in the Boussinesq approximation and via convective heat and mass transfer. The inverse problems are stated as the minimization of certain cost functionals at weak solutions to the original boundary value problem. Their solvability is proved, and optimality systems describing the necessary optimality conditions are derived. An analysis of the latter is used to establish sufficient conditions ensuring the local uniqueness and stability of solutions to the inverse extremum problems for particular cost functionals. 
@article{ZVMMF_2007_47_6_a10,
     author = {G. V. Alekseev},
     title = {Coefficient inverse extremum problems for stationary heat and mass transfer equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1055--1076},
     publisher = {mathdoc},
     volume = {47},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a10/}
}
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G. V. Alekseev. Coefficient inverse extremum problems for stationary heat and mass transfer equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1055-1076. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a10/