Geodesic
An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 127-136.

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

In the paper the problem of identification of two functions, one of which is under the integral sign in a hyperbolic equation and represents the medium's memory, the other one defines the regular part of an impulse source is considered. As additional information Fourier image trace solution of a direct problem on the hyperplane $y=0$ for two different values of transformation parameters is given. The estimate of stability of the solution of the inverse problem and the uniqueness theorems is proved.
Keywords: inverse problem, hyperbolic equation, stability, uniqueness. 
@article{JSFU_2009_2_2_a0,
     author = {Durdimurod K. Durdiev},
     title = {An {Identification} {Problem} of {Memory} {Function} of {a~Medium} and the {Form} of an {Impulse} {Source}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {127--136},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a0/}
}
TY  - JOUR
AU  - Durdimurod K. Durdiev
TI  - An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2009
SP  - 127
EP  - 136
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a0/
LA  - en
ID  - JSFU_2009_2_2_a0
ER  - 
%0 Journal Article
%A Durdimurod K. Durdiev
%T An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2009
%P 127-136
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a0/
%G en
%F JSFU_2009_2_2_a0
Durdimurod K. Durdiev. An Identification Problem of Memory Function of a~Medium and the Form of an Impulse Source. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 127-136. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a0/

[1] D. K. Durdiev, “An inverse problem for a three-dimensional wave equation in the medium with memory”, Math. Anal. and Disc. math., NGU, Novosibirsk, 1989, 19–26 (in Russian) | MR

[2] D. K. Durdiev, “To the question of correctness of one inverse problem for hyperbolic integro-differential equation”, Sib. Mat. Zh., 33:3 (1992), 69–77 (in Russian) | MR | Zbl

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

[4] J. Janno, L. Von Welfersdorf, “Inverse problems for identification of memory kernels in viscoelasticity”, Math. Methods in Appl. Sciences, 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, “On the problem of identifying the structure of layered medium and forms of an impulse source”, Sib. Mat. Zh., 48:4 (2007), 867–881 (in Russian) | MR | Zbl