Geodesic
Inverse problem of determining the absorption coefficient in the multidimensional heat equation with unlimited minor coefficients
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1183-1195

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The inverse problem of reconstructing the absorption coefficient (from $L_2$) in the multidimensional heat equation under an additional integral observation condition is studied. It is assumed that the minor coefficients belong to the Lebesgue space. For the solution to the inverse problem, sufficient conditions for existence, uniqueness, and stability to perturbations of input data are established. These conditions are formulated in the form of easy-to-check inequalities. 
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     author = {T. I. Bukharova and V. L. Kamynin},
     title = {Inverse problem of determining the absorption coefficient in the multidimensional heat equation with unlimited minor coefficients},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1183--1195},
     publisher = {mathdoc},
     volume = {55},
     number = {7},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a7/}
}
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T. I. Bukharova; V. L. Kamynin. Inverse problem of determining the absorption coefficient in the multidimensional heat equation with unlimited minor coefficients. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 7, pp. 1183-1195. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_7_a7/