Reconstruction of the emission coefficient in the nonlinear radiative transfer equation

Christian Klingenberg, Ru Yu Lai, And Qin Li

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we investigate an inverse problem for the radiative transfer equation that is coupled with a heat equation in a nonscattering medium in Rn, n ≥ 2. The two equations are coupled through a nonlinear blackbody emission term that is proportional to the fourth power of the temperature. By measuring the radiation intensity on the surface of the blackbody, we prove that the emission property of the system can be uniquely reconstructed. In particular, we design a reconstruction procedure that uses merely one set of experimental setup to fully recover the emission parameter.

Original languageEnglish (US)
Pages (from-to)91-106
Number of pages16
JournalSIAM Journal on Applied Mathematics
Volume81
Issue number1
DOIs
StatePublished - 2021

Bibliographical note

Funding Information:
\ast Received by the editors June 26, 2020; accepted for publication (in revised form) October 7, 2020; published electronically January 14, 2021. https://doi.org/10.1137/20M1348339 Funding: The work of the first author was partially supported by ERASMUS+. The work of the second author was partially supported by the NSF grant DMS-1714490. The work of the third author was partially supported by the NSF grant DMS-1750488. \dagger Department of Mathematics, Wu\"rzburg University, Wu\"rzburg 97074, Germany (klingen@ mathematik.uni-wuerzburg.de). \ddagger School of Mathematics, University of Minnesota, Minneapolis, MN 55455 USA (rylai@umn.edu). \S Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53705 USA (qinli@math.wisc.edu).

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.

Keywords

  • Blackbody emission
  • Inverse problem
  • Nonlinear radiative transfer equation
  • Stability
  • Uniqueness

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