Geodesic
Parabolic equations with unknown time-dependent coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 961-972

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The solvability of inverse problems of finding the coefficients of a parabolic equation together with solving this equation is studied. In these problems, certain additional conditions on the boundary are used as overdetermination conditions. Existence and uniqueness theorems for regular solutions of such problems are proven. 
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     author = {A. I. Kozhanov},
     title = {Parabolic equations with unknown time-dependent coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {961--972},
     publisher = {mathdoc},
     volume = {57},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a4/}
}
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A. I. Kozhanov. Parabolic equations with unknown time-dependent coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 6, pp. 961-972. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_6_a4/