Geodesic
An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 28-40.

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

For the equation of wave propagation in the half-space filled with some medium, we consider the problem of determining the wave propagation velocity which depends only on the variable $y$ and the memory functions of the medium. There is a point-like pulse source on the boundary of the half-space. We show that both unknown functions of one variable are uniquely determined by the Fourier image with respect to $x$ of the solution to the direct problem on the boundary of the half-space. We estimate the stability of the solution to the problem.
Keywords: inverse problem, stability, uniqueness.
Mots-clés : Fourier transform 
@article{SJIM_2009_12_3_a3,
     author = {D. K. Durdiev},
     title = {An {Inverse} {Problem} for {Determining} {Two} {Coefficients} in {an~Integrodifferential} {Wave} {Equation}},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {28--40},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/}
}
TY  - JOUR
AU  - D. K. Durdiev
TI  - An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2009
SP  - 28
EP  - 40
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/
LA  - ru
ID  - SJIM_2009_12_3_a3
ER  - 
%0 Journal Article
%A D. K. Durdiev
%T An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2009
%P 28-40
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/
%G ru
%F SJIM_2009_12_3_a3
D. K. Durdiev. An Inverse Problem for Determining Two Coefficients in an~Integrodifferential Wave Equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 28-40. http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a3/

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

[2] Yakhno V. G., Obratnye zadachi dlya differentsialnykh uravnenii uprugosti, Nauka, Novosibirsk, 1990 | MR | Zbl

[3] Lorensi A., “An identification problem related to a nonlinear hyperbolic integro-differential equation”, Nonlinear Analysis: Theory, Methods and Applications, 22 (1994), 297–321 | MR

[4] Janno J., Von Welfersdorf L., “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] Bukhgeim A. L., Kalinina N. I., “Globalnaya skhodimost metoda Nyutona v obratnykh zadachakh vosstanovleniya pamyati”, Sib. mat. zhurn., 38:5 (1997), 1018–1033 | MR | Zbl

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

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

[8] Durdiev D. K., “Some multidimensional inverse problems of memory determination in hyperbolic equations”, J. Math. Physics, Analysis, Geometry, 3:4 (2007), 411–423 | MR

[9] Durdiev D. K., “Globalnaya razreshimost odnoi obratnoi zadachi dlya integrodifferentsialnogo uravneniya elektrodinamiki”, Differents. uravneniya, 44:7 (2008), 867–873 | MR