Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data

Özlem Kaytmaz; Muhammed Hasdemir

doi:10.28979/jarnas.1965426

Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data

Abstract

This paper addresses an inverse source problem for a linearized Boltzmann equation, a model that arises in important applications such as rarefied gas dynamics, radiative transfer, and particle transport. The aim is to determine an unknown source term from the model equation together with appropriate observational data. Under structural convexity assumptions on the Hamiltonian and an L2-boundedness condition on the linearized collision operator, uniqueness for the inverse source problem is proved using boundary trace and gradient data. The proof relies on a pointwise energy identity for the transport operator combined with estimates for the collision contribution.

Keywords

Supporting Institution

This research received no specific grant from any funding agency, commercial, or not-for-profit sectors.

Ethical Statement

This study does not involve human participants, animals, or sensitive personal data. Therefore, ethical approval was not required.

Thanks

The authors would like to express their sincere thanks to the editor for the careful consideration and handling of the manuscript.

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Özlem Kaytmaz
0000-0003-0420-007X
Türkiye

Muhammed Hasdemir ^*
0000-0001-5901-3699
Türkiye

Publication Date

September 30, 2026

Submission Date

June 6, 2026

Acceptance Date

August 5, 2026

Published in Issue

Year 2026 Volume: 12 Number: 3

DOI

https://doi.org/10.28979/jarnas.1965426

IZ

https://izlik.org/JA44XL46AZ

Cite

RIS / Bibtex

APA

Kaytmaz, Ö., & Hasdemir, M. (2026). Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data. Journal of Advanced Research in Natural and Applied Sciences, 12(3), 325-336. https://doi.org/10.28979/jarnas.1965426

AMA

1.Kaytmaz Ö, Hasdemir M. Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data. JARNAS. 2026;12(3):325-336. doi:10.28979/jarnas.1965426

Chicago

Kaytmaz, Özlem, and Muhammed Hasdemir. 2026. “Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation With Trace and Gradient Data”. Journal of Advanced Research in Natural and Applied Sciences 12 (3): 325-36. https://doi.org/10.28979/jarnas.1965426.

EndNote

Kaytmaz Ö, Hasdemir M (September 1, 2026) Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data. Journal of Advanced Research in Natural and Applied Sciences 12 3 325–336.

IEEE

[1]Ö. Kaytmaz and M. Hasdemir, “Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data”, JARNAS, vol. 12, no. 3, pp. 325–336, Sept. 2026, doi: 10.28979/jarnas.1965426.

ISNAD

Kaytmaz, Özlem - Hasdemir, Muhammed. “Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation With Trace and Gradient Data”. Journal of Advanced Research in Natural and Applied Sciences 12/3 (September 1, 2026): 325-336. https://doi.org/10.28979/jarnas.1965426.

JAMA

1.Kaytmaz Ö, Hasdemir M. Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data. JARNAS. 2026;12:325–336.

MLA

Kaytmaz, Özlem, and Muhammed Hasdemir. “Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation With Trace and Gradient Data”. Journal of Advanced Research in Natural and Applied Sciences, vol. 12, no. 3, Sept. 2026, pp. 325-36, doi:10.28979/jarnas.1965426.

Vancouver

1.Özlem Kaytmaz, Muhammed Hasdemir. Uniqueness for an Inverse Source Problem in a Linearized Boltzmann Equation with Trace and Gradient Data. JARNAS. 2026 Sep. 1;12(3):325-36. doi:10.28979/jarnas.1965426

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