Inverse problems of finding the lowest coefficient in the elliptic equation

Alexander I. Kozhanov ; Tatyana N. Shipina

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 528-542.

Résumé

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.

Détail

Keywords: unknown coefficient, spatial integral condition, boundary integral condition, uniqueness.
Mots-clés : elliptic equation, existence

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