Geodesic
Parabolic equations with an unknown time-dependent coefficient
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2168-2184

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The solvability of nonlinear inverse problems of determining the solution $u(x,t)$ and the coefficients $p(t)$ and $q(t)$ in parabolic equations subject to the boundary conditions of the first or second initial-boundary value problems and an integral overdetermination condition is investigated. Existence theorems for the regular solution are proved. 
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     author = {A. I. Kozhanov},
     title = {Parabolic equations with an unknown time-dependent coefficient},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2168--2184},
     publisher = {mathdoc},
     volume = {45},
     number = {12},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a6/}
}
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A. I. Kozhanov. Parabolic equations with an unknown time-dependent coefficient. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2168-2184. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a6/