Stability Estimates for Solution of Neumann-Type Overdetermined Elliptic Problem. (3rd October 2017)

• Record Type: Journal Article
• Authors: Ashyralyyev, Charyyar
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 10(2017)
• Page Start: 1226
• Page End: 1243
• Publication Date: 2017-10-03
• Subjects: Coercive stability -- difference scheme -- inverse problem -- overdetermination -- stability; 35N25 -- 39A14 -- 65J22; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1316993
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This paper addresses estimation of the solution of inverse problem for the elliptic type equation with second kind boundary conditions and Neumann-type overdetermination at the interior point. We prove various estimates for the solution of this identification problem. Then, the first order accuracy stable difference scheme is studied. The stability, almost coercive stability, and coercive stability inequalities for its solution are obtained. The theoretical results can be applied to investigate identification problems for multidimensional elliptic equation with different kind of boundary conditions.