TY - JOUR

T1 - Inverse problems of finding the lowest coefficient in the elliptic equation

AU - Kozhanov, Alexander I.

AU - Shipina, Tatyana N.

N1 - Funding Information: The work is supported by the Russian Foundation basic research (grant 18-01-00620). Publisher Copyright: © Siberian Federal University. All rights reserved.

PY - 2021

Y1 - 2021

N2 - The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2∆u − q(t)u = f(x, t) (x = (x1, …, xn) ∈ Ω ⊂ ℝn, t ∈ (0, T ), 0 < T < +∞, ∆ — operator Laplace on x1, …, xn). 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.

AB - The article is devoted to the study of problems of finding the non-negative coefficient q(t) in the elliptic equation utt + a2∆u − q(t)u = f(x, t) (x = (x1, …, xn) ∈ Ω ⊂ ℝn, t ∈ (0, T ), 0 < T < +∞, ∆ — operator Laplace on x1, …, xn). 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.

KW - Boundary integral condition

KW - Elliptic equation

KW - Existence

KW - Spatial integral condition

KW - Uniqueness

KW - Unknown coefficient

UR - http://www.scopus.com/inward/record.url?scp=85115147762&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=46403004

U2 - 10.17516/1997-1397-2021-14-4-528-542

DO - 10.17516/1997-1397-2021-14-4-528-542

M3 - Article

AN - SCOPUS:85115147762

VL - 14

SP - 528

EP - 542

JO - Journal of Siberian Federal University - Mathematics and Physics

JF - Journal of Siberian Federal University - Mathematics and Physics

SN - 1997-1397

IS - 4

M1 - 15

ER -