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Domain Identification for Inverse Problem via Conformal Mapping and Fixed Point Methods in Two Dimensions
Author
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-08-25
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
In this paper, we present a survey of the inverse eigenvalue problem for a Laplacian equation based on available Cauchy data on a known part Γ0 and a homogeneous Dirichlet condition on an unknown part Γ0 of the boundary of a bounded domain, Ω⊂ℝN.
We consider variations in the eigenvalues and propose a conformal mapping tool to reconstruct a part of the boundary curve of the two-dimensional bounded domain based on the Cauchy data of a holomorphic function that maps the unit disk onto the unknown domain.
The boundary values of this holomorphic function are obtained by solving a nonlocal differential Bessel equation.
Then, the unknown boundary is obtained as the image of the boundary of the unit disk by solving an ill-posed Cauchy problem for holomorphic functions via a regularized power expansion.
The Cauchy data were restricted to a nonvanishing function and to the normal derivatives without zeros.
We prove the existence and uniqueness of the holomorphic function being considered and use the fixed-point method to numerically analyze the results of convergence.
We’ll calculate the eigenvalues and compare the result with the shape obtained via minimization functional method, as developed in a previous study.
Further, we’ll observe via simulations the shape of Γ and if it preserves its properties with varying the eigenvalues.
American Psychological Association (APA)
Ndiaye, Fagueye. 2020. Domain Identification for Inverse Problem via Conformal Mapping and Fixed Point Methods in Two Dimensions. Abstract and Applied Analysis،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1119843
Modern Language Association (MLA)
Ndiaye, Fagueye. Domain Identification for Inverse Problem via Conformal Mapping and Fixed Point Methods in Two Dimensions. Abstract and Applied Analysis No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1119843
American Medical Association (AMA)
Ndiaye, Fagueye. Domain Identification for Inverse Problem via Conformal Mapping and Fixed Point Methods in Two Dimensions. Abstract and Applied Analysis. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1119843
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119843