On the transport method for hybrid inverse problems

Francis J. Chung, Jeremy G. Hoskins, John C. Schotland

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

There are several hybrid inverse problems for equations of the form ∇ · D(x) ∇ u - σ (x) u = 0in which we want to obtain the coefficients D and σ on a domain Ω when the solutions u are known. One approach is to use two solutions u1 and u2 to obtain a transport equation for the coefficient D, and then solve this equation inward from the boundary along the integral curves of a vector field X defined by u1 and u2. Bal and Ren have shown that for any nontrivial choices of u1 and u2, this method suffices to recover the coefficients almost everywhere on a dense set in Ω Bal and Ren in (Inv Prob 075003 [3]). This article presents an alternate proof of the same result from a dynamical systems point of view.

Original languageEnglish
Title of host publicationMathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019
EditorsLarisa Beilina, Maïtine Bergounioux, Michel Cristofol, Anabela Da Silva, Amelie Litman
Pages15-20
Number of pages6
DOIs
StatePublished - 2020
EventConference on Mathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019 - Marseille, France
Duration: Apr 1 2019Apr 5 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume328
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceConference on Mathematical and Numerical Approaches for Multi-Wave Inverse Problems, CIRM 2019
Country/TerritoryFrance
CityMarseille
Period4/1/194/5/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

Keywords

  • Hybrid inverse problems
  • Reconstruction of coefficients
  • Transport equation

ASJC Scopus subject areas

  • General Mathematics

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