Scalar and vector tomography for the weighted transport equation with application to helioseismology-Reference-Cited by-同舟云学术

Scalar and vector tomography for the weighted transport equation with application to helioseismology

Published:2022-04-08 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Thompson Nathan L.¹^ORCID,Bukhgeim Alexander L.¹

Affiliation:

1. Department of Mathematics,Statistics,and Physics , Wichita State University , 1845 N. Fairmount , Wichita , KS 67260 , USA

Abstract

Abstract Motivated by the application to helioseismology, we demonstrate uniqueness and stability for a class of inverse problems of the weighted transport equation. Using 𝐴-analytic functions, this inverse problem is expressed as a Cauchy problem. In this form, we show that, for a finite even trigonometric polynomial weight function, the resulting system is well-conditioned numerically and permits a Carleman-like estimate with boundary terms.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2021-0001/pdf

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