Geodesic
Identification of a boundary condition in the heat and mass transfer problems
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 234-253

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We consider well-posedness in Sobolev spaces of inverse problems of recovering a function occurring in the Robin boundary condition in the parabolic case. The existence and uniqueness theorem are exhibited. The proof relies on a priori estimates obtained and the method of continuation in a parameter. The method is constructive and the approach allows to develop numerical methods for solving the problem.
Keywords: inverse problem, heat and mass transfer, parabolic equation, Robin boundary condition. 
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     author = {S. G. Pyatkov and V. A. Baranchuk},
     title = {Identification of a boundary condition in the heat and mass transfer problems},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {234--253},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a6/}
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S. G. Pyatkov; V. A. Baranchuk. Identification of a boundary condition in the heat and mass transfer problems. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 2, pp. 234-253. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_2_a6/