Geodesic
The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 398-411

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The unique solvability of the inverse problem of recovering the source function in a nonuniformly parabolic equation with many independent variables in a bounded domain is proved. As an additional condition, the integral observation condition is given. The unknown source function can be found by iteration from the operator equation with contraction operator. An example of an the inverse problem for which the results proved in this paper are applicable is presented. The results obtained for the inverse problem are based on the preliminary study of the unique solvability of the corresponding direct problem, which is also of interest in itself.
Keywords: the inverse problems, nonuniformly parabolic equations, integral observation. 
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     author = {V. L. Kamynin},
     title = {The {Inverse} {Problem} of {Recovering} the {Source} {Function} in a {Multidimensional} {Nonuniformly} {Parabolic} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {398--411},
     publisher = {mathdoc},
     volume = {112},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a8/}
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V. L. Kamynin. The Inverse Problem of Recovering the Source Function in a Multidimensional Nonuniformly Parabolic Equation. Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 398-411. http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a8/