Inverse problems of finding the lowest coefficient in the elliptic equation

Alexander I. Kozhanov; Tatyana N. Shipina

doi:10.17516/1997-1397-2021-14-4-528-542

Inverse problems of finding the lowest coefficient in the elliptic equation

Alexander I. Kozhanov, Tatyana N. Shipina

Research output: Contribution to journal › Article › peer-review

Abstract

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

Translated title of the contribution	Обратные задачи восстановления младшего коэффициента в эллиптическом уравнении
Original language	English
Article number	15
Pages (from-to)	528-542
Number of pages	15
Journal	Journal of Siberian Federal University - Mathematics and Physics
Volume	14
Issue number	4
DOIs	https://doi.org/10.17516/1997-1397-2021-14-4-528-542
Publication status	Published - 2021

Keywords

Boundary integral condition
Elliptic equation
Existence
Spatial integral condition
Uniqueness
Unknown coefficient

OECD FOS+WOS

1.01 MATHEMATICS

State classification of scientific and technological information

27 MATHEMATICS

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

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title = "Inverse problems of finding the lowest coefficient in the elliptic equation",

abstract = "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.",

keywords = "Boundary integral condition, Elliptic equation, Existence, Spatial integral condition, Uniqueness, Unknown coefficient",

author = "Kozhanov, {Alexander I.} and Shipina, {Tatyana N.}",

note = "Funding Information: The work is supported by the Russian Foundation basic research (grant 18-01-00620). Publisher Copyright: {\textcopyright} Siberian Federal University. All rights reserved.",

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AU - Shipina, Tatyana N.

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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

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JO - Journal of Siberian Federal University - Mathematics and Physics

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SN - 1997-1397

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ER -

Inverse problems of finding the lowest coefficient in the elliptic equation

Abstract

Keywords

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