Geodesic
Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 827-833

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

We consider The Cauchy problem for the wave equation with an unknown right hand side, that rapidly oscillates in time. This right hand side is reconstructed from the three-term asymptotics of a solution, which are given at one point of the domain. In this case, an approach developed earlier by one of the authors of this article is used to solve the inverse problems with rapidly oscillating data.
Keywords: wave equation, Cauchy problem, asymptotics of a solution, reconstruction of an unknown high-frequency source term. 
@article{SEMR_2021_18_2_a45,
     author = {E. V. Korablina and V. B. Levenshtam},
     title = {Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. {Case} of the {Cauchy} problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {827--833},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a45/}
}
TY  - JOUR
AU  - E. V. Korablina
AU  - V. B. Levenshtam
TI  - Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 827
EP  - 833
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a45/
LA  - en
ID  - SEMR_2021_18_2_a45
ER  - 
%0 Journal Article
%A E. V. Korablina
%A V. B. Levenshtam
%T Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 827-833
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a45/
%G en
%F SEMR_2021_18_2_a45
E. V. Korablina; V. B. Levenshtam. Reconstruction of a high-frequency source term of the wave equation from the asymptotics of the solution. Case of the Cauchy problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 827-833. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a45/