Geodesic
Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 29-36

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

In this paper, we consider the Cauchy problem for the telegraph equation. The lower coefficient and the right-hand side of the equation oscillate in time with a high frequency, the amplitude of the lower coefficient is small, namely, is inversely proportional to the frequency, and the right-hand side is unknown. We examine the problem on the recovery of the right-hand side from the three-term asymptotics of the solution given at some point in space. For this purpose, we use a nonclassical algorithm for solving inverse coefficient problems with rapidly oscillating data.
Keywords: inverse problem, asymptotic methods, telegraph equation, rapidly oscillating data. 
@article{INTO_2022_208_a4,
     author = {E. V. Korablina and V. B. Levenshtam},
     title = {Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {29--36},
     publisher = {mathdoc},
     volume = {208},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_208_a4/}
}
TY  - JOUR
AU  - E. V. Korablina
AU  - V. B. Levenshtam
TI  - Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 29
EP  - 36
VL  - 208
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_208_a4/
LA  - ru
ID  - INTO_2022_208_a4
ER  - 
%0 Journal Article
%A E. V. Korablina
%A V. B. Levenshtam
%T Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 29-36
%V 208
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_208_a4/
%G ru
%F INTO_2022_208_a4
E. V. Korablina; V. B. Levenshtam. Asymptotic problem of restoring the high-frequency right-hand side of the telegraph equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 29-36. http://geodesic.mathdoc.fr/item/INTO_2022_208_a4/