Geodesic
An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport
Matematičeskie zametki SVFU, Tome 27 (2020) no. 4, pp. 3-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: tomography, inverse problems, unknown boundary, discontinuous coefficients, indicator of heterogeneity.
Mots-clés : transport equation 
@article{SVFU_2020_27_4_a0,
     author = {E. Yu. Balakina},
     title = {An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {3--13},
     year = {2020},
     volume = {27},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_4_a0/}
}
TY  - JOUR
AU  - E. Yu. Balakina
TI  - An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport
JO  - Matematičeskie zametki SVFU
PY  - 2020
SP  - 3
EP  - 13
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SVFU_2020_27_4_a0/
LA  - ru
ID  - SVFU_2020_27_4_a0
ER  - 
%0 Journal Article
%A E. Yu. Balakina
%T An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport
%J Matematičeskie zametki SVFU
%D 2020
%P 3-13
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/SVFU_2020_27_4_a0/
%G ru
%F SVFU_2020_27_4_a0
E. Yu. Balakina. An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport. Matematičeskie zametki SVFU, Tome 27 (2020) no. 4, pp. 3-13. http://geodesic.mathdoc.fr/item/SVFU_2020_27_4_a0/