Geodesic
On some classes of inverse problems on determining source functions for heat and mass transfer systems
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 23-42

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In this paper, we considers the question on the well-posedness in Sobolev spaces of the problem of determining the source function in a heat and mass transfer system consisting of the Navier–Stokes system, a parabolic equation for temperature, and a parabolic system for the concentrations of substances being transferred. Weighted integrals solution over the spatial domain serve as overdetermination conditions. A local (in time) existence theorem for the solution of the problem in the nonlinear case is proved and stability estimates are obtained; for a linearized system, a global existence theorem is obtained.
Keywords: heat and mass transfer system, inverse problem, integral overdetermination, uniqueness, initial-boundary-value problem.
Mots-clés : existence 
@article{INTO_2020_188_a2,
     author = {S. G. Pyatkov},
     title = {On some classes of inverse problems on determining source functions for heat and mass transfer systems},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {23--42},
     publisher = {mathdoc},
     volume = {188},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_188_a2/}
}
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S. G. Pyatkov. On some classes of inverse problems on determining source functions for heat and mass transfer systems. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Modeling, Tome 188 (2020), pp. 23-42. http://geodesic.mathdoc.fr/item/INTO_2020_188_a2/