Geodesic
Inverse problems of finding the lowest coefficient in the elliptic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 528-542

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The article is devoted to the study of problems of finding the non-negative coefficient $q(t)$ in the elliptic equation $$u_{tt}+a^2\Delta u-q(t)u=f(x,t)$$ ($x=(x_1,\ldots,x_n)\in\Omega\subset \mathbb{R}^n$, $t\in (0,T)$, $0$, $\Delta$ — operator Laplace on $x_1, \ldots, x_n$). These problems contain the usual boundary conditions and additional condition ( spatial integral overdetermination condition or boundary integral overdetermination condition). The theorems of existence and uniqueness are proved.
Keywords: unknown coefficient, spatial integral condition, boundary integral condition, uniqueness.
Mots-clés : elliptic equation, existence 
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     title = {Inverse problems of finding the lowest coefficient in the elliptic equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Alexander I. Kozhanov; Tatyana N. Shipina. Inverse problems of finding the lowest coefficient in the elliptic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 528-542. http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a14/