Work

Inverse Problems of Recovering Lower-Order Coefficients from Boundary Integral Data

Year: 2025

Type: article

Abstract: We study inverse problems of identification of lower-order coefficients in a second-order parabolic equation. The coefficients are sought in the form of a finite series segment with unknown coefficients, depending on time. The linear case is also considered. Overdetermination conditions are the integrals over the boundary of a solution’s domain with weights. We focus on existence and uniqueness theorems and stability estimates for solutions to these inverse problems. An operator equation to which the problem is reduced is studied with the use of the contraction mapping principle. A solution belongs to some Sobolev space and has all generalized derivatives occurring into the equation summable to some power. The method of the proof is constructive, and it can be used for developing new numerical algorithms for solving the problem.

Source: Axioms

DOI: 10.3390/axioms14020116

Authors: Sergey Pyatkov, Oleg Soldatov

Institutions: Yugra State University, Academy of Sciences of the Republic of Sakha

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Ministry of Science and Higher Education of the Russian Federation