Inverse source problems in transport equations with external forces

Ru Yu Lai; Hanming Zhou

doi:10.1016/j.jde.2021.09.011

Inverse source problems in transport equations with external forces

Ru Yu Lai, Hanming Zhou

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.

Original language	English (US)
Pages (from-to)	728-752
Number of pages	25
Journal	Journal of Differential Equations
Volume	302
DOIs	https://doi.org/10.1016/j.jde.2021.09.011
State	Published - Nov 25 2021

Bibliographical note

Funding Information:
RL was partially supported by NSF grant DMS-2006731 . HZ was partly supported by NSF grant DMS-2109116 .

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

Attenuated X-ray transform
Inverse source problems
Santalo's formula
Transport equations

Publisher link

10.1016/j.jde.2021.09.011

Find It

Find It at U of M Libraries

Cite this

@article{09d6178b04594bbc9f199f79a2a3c672,

title = "Inverse source problems in transport equations with external forces",

abstract = "This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.",

keywords = "Attenuated X-ray transform, Inverse source problems, Santalo's formula, Transport equations",

author = "Lai, {Ru Yu} and Hanming Zhou",

note = "Funding Information: RL was partially supported by NSF grant DMS-2006731 . HZ was partly supported by NSF grant DMS-2109116 . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = nov,

day = "25",

doi = "10.1016/j.jde.2021.09.011",

language = "English (US)",

volume = "302",

pages = "728--752",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Inverse source problems in transport equations with external forces

AU - Lai, Ru Yu

AU - Zhou, Hanming

PY - 2021/11/25

Y1 - 2021/11/25

N2 - This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.

AB - This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse problems, generic injectivity and a stability estimate of the source are derived. The analysis employs the Fredholm theorem and the Santalo's formula.

KW - Attenuated X-ray transform

KW - Inverse source problems

KW - Santalo's formula

KW - Transport equations

UR - http://www.scopus.com/inward/record.url?scp=85115199170&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85115199170&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2021.09.011

DO - 10.1016/j.jde.2021.09.011

M3 - Article

AN - SCOPUS:85115199170

SN - 0022-0396

VL - 302

SP - 728

EP - 752

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Inverse source problems in transport equations with external forces

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this