Geodesic
An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport
Matematičeskie zametki SVFU, Tome 27 (2020), pp. 3-13.

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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_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},
     publisher = {mathdoc},
     volume = {27},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2020_27_a0/}
}
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E. Yu. Balakina. An algorithm for inhomogeneous medium reconstruction in case of unsteady particle transport. Matematičeskie zametki SVFU, Tome 27 (2020), pp. 3-13. http://geodesic.mathdoc.fr/item/SVFU_2020_27_a0/