Алгоритм реконструкции неоднородной среды в случае нестационарного переноса частиц в среде

Translated title of the contribution: An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the problem of X-ray tomography that is the inverse problem for the non-stationary differential transport equation. We study an equation in which the coefficients and the unknown function depend on time, while the coefficients can undergo a discontinuity of the first kind in the spatial variable. The desired object is the set on which the coefficients of the transport equation undergo a discontinuity, that corresponds to the search of boundaries between various substances contained in the probed medium. To this end, we consider a special function-an indicator of medium heterogeneity. Using the explicit solutions of the direct and inverse problems, we can indicate the main property of that function: it takes unlimited values on the desired sets. Our main result is a numerical demonstration of the properties of that function. Several examples are given.

Translated title of the contributionAn algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport
Original languageRussian
Article number1
Pages (from-to)3-13
Number of pages11
JournalMathematical Notes of NEFU
Volume27
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Discontinuous coefficients
  • Indicator of heterogeneity
  • Inverse problems
  • Tomography
  • Transport equation
  • Unknown boundary

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES
  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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