An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with Cauchy data
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 186-199.

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

The existence and uniqueness of solution of the identification problem for multi-dimensional parabolic equation with source function of the special form in the case of Cauchy's data has been proved in this paper.
Keywords: inverse problem, identification of coefficient at source function, multi-dimensional parabolic equation, method of weak approximation, existence and uniqueness of solution, Cauchy problem.
@article{JSFU_2013_6_2_a5,
     author = {Igor V. Frolenkov and Ekaterina N. Kriger},
     title = {An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with {Cauchy} data},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {186--199},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a5/}
}
TY  - JOUR
AU  - Igor V. Frolenkov
AU  - Ekaterina N. Kriger
TI  - An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with Cauchy data
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2013
SP  - 186
EP  - 199
VL  - 6
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a5/
LA  - en
ID  - JSFU_2013_6_2_a5
ER  - 
%0 Journal Article
%A Igor V. Frolenkov
%A Ekaterina N. Kriger
%T An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with Cauchy data
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2013
%P 186-199
%V 6
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a5/
%G en
%F JSFU_2013_6_2_a5
Igor V. Frolenkov; Ekaterina N. Kriger. An identification problem of coefficient in the special form at source function for multi-dimensional parabolic equation with Cauchy data. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 186-199. http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a5/

[1] Yu. Ya. Belov, I. V. Frolenkov, “Coefficient Identification Problems for Semilinear Parabolic Equations”, Doklady Mathematics, 72:2 (2005), 737–739 | Zbl

[2] Yu. Ya. Belov, Inverse Problems for Partial Differential Equations, VSP, Utrecht, 2002 | MR | Zbl

[3] N. N. Yanenko, The method of fractional steps for solving multi-dimensional problems of mathematical physics, Novosibirsk, 1967 (in Russian)

[4] I. V. Frolenkov, E. N. Kriger, “An identification problem of the source function of the special form in two-dimensional parabolic equation”, Journal of Siberian Federal University. Mathematics Physics, 3:4 (2010), 556–564 (in Russian)

[5] E. N. Kriger, I. V. Frolenkov, “An stabilization of solution of the one inverse problem for two-dimensional parabolic equation”, The international conference dedicated to the 80th anniversary of the birthday of academician M. M. Lavrent'ev “Inverse and ill-posed problems of mathematical physics” (Novosibirsk, Russia, 5–12 August 2012), Abstracts, 2012, 87–88 (in Russian)

[6] E. N. Kriger, I. V. Frolenkov, “An identification problem of the source function of the special form in two-dimensional parabolic equation”, The XLIX international scientific students' conference “Student and scientific-technical progress”: Mathematics (Novosibirsk State University, Novosibirsk, 16–20 April 2011), Abstracts, 2011, 50 (in Russian)

[7] O. A. Afinogenova, Yu. Ya. Belov, I. V. Frolenkov, “Stabilization of the Solution to the Identification Problem of the Source Function for a One-Dimensional Parabolic Equation”, Doklady Mathematics, 79:1 (2009), 70–72 | DOI | MR | Zbl

[8] I. V. Frolenkov, G. V. Romanenko, “An Representation of the Solution of the Inverse Problem for a Multidimensional Parabolic Equation with Initial Data in the Form of a Product”, Journal of Siberian Federal University. Mathematics Physics, 5:1 (2012), 122–131 (in Russian)

[9] I. V. Frolenkov, G. V. Romanenko, “About solution of an inverse problem for a multidimensional parabolic equation”, Sibirskii Zhurnal Industrial'noi Matematiki, 15:2(50) (2012), 139–146 (in Russian)

[10] O. N. Cherepanova, T. N. Shipina, “An identification problem of the source function for a parabolic equation”, Journal of Siberian Federal University. Mathematics Physics, 2:3 (2009), 370–375 (in Russian)

[11] A. I. Prilepko, D. G. Orlovsky, I. A. Vasin, Methods for solving inverse problems in mathematical physics, Marcel Dekker, New York, 2000 | MR | Zbl