Scalar and vector tomography for the weighted transport equation with application to helioseismology
Thompson, Nathan L. Bukhgeym, Alexander L.
Thompson, Nathan L.
Bukhgeym, Alexander L.
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2022-04-08
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Scalar and vector tomography,Helioseismology,Polynomial weight,Carleman estimates
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Thompson, Nathan L. and Bukhgeim, Alexander L.. "Scalar and vector tomography for the weighted transport equation with application to helioseismology" Journal of Inverse and Ill-posed Problems, vol. , no. , 2022. https://doi.org/10.1515/jiip-2021-0001
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.
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De Gruyter Open Ltd
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Journal of Inverse and Ill Posed Problems
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1569-3945