Geodesic
Stability of an inverse problem for transport equation with discrete data
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 337-345.

Voir la notice de l'article provenant de la source Math-Net.Ru

A validity of numerical algorithms is under investigation in this article. Namely, stability for twodimensional problem of restoring the right-hand side in the transport equation by discrete data is considered. It is suggested that the radiation incident on the boundary is omitted. The outgoing radiation is known at discrete numbers on the boundary. Stability theorems for two problem formulations are proved. In the former case an interparticle collision is not considered. In the latter case the transport equation is considered with the integral term and absorption, and scattering properties of the medium are taking into account. 
@article{SJVM_1998_1_4_a4,
     author = {O. A. Klimenko},
     title = {Stability of an inverse problem for transport equation with discrete data},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {337--345},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a4/}
}
TY  - JOUR
AU  - O. A. Klimenko
TI  - Stability of an inverse problem for transport equation with discrete data
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 1998
SP  - 337
EP  - 345
VL  - 1
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a4/
LA  - en
ID  - SJVM_1998_1_4_a4
ER  - 
%0 Journal Article
%A O. A. Klimenko
%T Stability of an inverse problem for transport equation with discrete data
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 1998
%P 337-345
%V 1
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a4/
%G en
%F SJVM_1998_1_4_a4
O. A. Klimenko. Stability of an inverse problem for transport equation with discrete data. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 4, pp. 337-345. http://geodesic.mathdoc.fr/item/SJVM_1998_1_4_a4/

[1] Muhometov R. G., “Stability estimate for one problem of computer tomography”, The questions of well-posedness of analysis problems, Siberian Division. Institute of Math., Novosibirsk, 1989, 122–124 (In Russian)

[2] Zav'yalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Methods of spline functions, Nauka, M., 1980 (In Russian) | MR

[3] Romanov V. G., “Conditional stability estimates for the two-dimensional problem of restoring the right-hand side and absorption in the transport equation”, SMJ, 35:6 (1994), 1184–1201 | MR | Zbl