Geodesic
The problem of determining of the source function and of the leading coefficient in the many-dimensional semilinear parabolic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 497-506

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We consider the problem of determining the source function and the leading coefficient in a multidimensional semilinear parabolic equation with overdetermination conditions given on two different hypersurfaces. The existence and uniqueness theorem for the classical solution of the inverse problem in the class of smooth bounded functions is proved. A condition is found for the dependence of the upper bound of the time interval, in which there is a unique solution to the inverse problem, on the input data.
Keywords: inverse problem, overdetermination conditions, semilinear multidimensional parabolic equation, Cauchy problem, weak approximation method, input data
Mots-clés : identification of coefficients. 
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     title = {The problem of determining of the source function and of the leading coefficient in the many-dimensional semilinear parabolic equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a11/}
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Svetlana V. Polyntseva; Kira I. Spirina. The problem of determining of the source function and of the leading coefficient in the many-dimensional semilinear parabolic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 497-506. http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a11/