Geodesic
The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 202-212.

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

Consider the problem of finding two coefficients one of which is under the sign of the integral in the hyperbolic equation and represents the memory of a medium and the other determines the regular part of an impulse source. Additionally, the Fourier transform of the trace of the solution of the direct problem on the hyperplane $y=0$ for two different values of the transformation parameter is given. We establish an estimate of the stability of the solution of the inverse problem under consideration and also the uniqueness theorem.
Keywords: hyperbolic equation, impulse source, memory of a medium, method of successive approximations, $\delta$ function.
Mots-clés : Fourier transform, Volterra equation 
@article{MZM_2009_86_2_a5,
     author = {D. K. Durdiev},
     title = {The {Problem} of {Determining} a {Function} of the {Memory} of a {Medium} and of the {Regular} {Part} of a {Pulsed} {Source}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {202--212},
     publisher = {mathdoc},
     volume = {86},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a5/}
}
TY  - JOUR
AU  - D. K. Durdiev
TI  - The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source
JO  - Matematičeskie zametki
PY  - 2009
SP  - 202
EP  - 212
VL  - 86
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a5/
LA  - ru
ID  - MZM_2009_86_2_a5
ER  - 
%0 Journal Article
%A D. K. Durdiev
%T The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source
%J Matematičeskie zametki
%D 2009
%P 202-212
%V 86
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a5/
%G ru
%F MZM_2009_86_2_a5
D. K. Durdiev. The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 202-212. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a5/

[1] D. K. Durdiev, “Obratnaya zadacha dlya trekhmernogo volnovogo uravneniya v srede s pamyatyu”, Matematicheskii analiz i diskretnaya matematika, NGU, Novosibirsk, 1989, 19–26 | MR | Zbl

[2] D. K. Durdiev, “K voprosu o korrektnosti odnoi obratnoi zadachi dlya giperbolicheskogo integrodifferentsialnogo uravneniya”, Sib. matem. zhurn., 33:3 (1992), 69–77 | MR | Zbl

[3] A. Lorenzi, “An identification problem related to a nonlinear hyperbolic integro-differential equation”, Nonlinear Anal., 22:1 (1994), 21–44 | MR | Zbl

[4] J. Janno, L. Von Wolfersdorf, “Inverse problems for identification of memory kernels in viscoelasticity”, Math. Methods Appl. Sci., 20:4 (1997), 291–314 | 3.0.CO;2-W class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[5] V. G. Romanov, “O zadache opredeleniya struktury sloistoi sredy i formy impulsnogo istochnika”, Sib. matem. zhurn., 48:4 (2007), 867–881 | MR | Zbl

[6] V. G. Romanov, Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR | Zbl