Geodesic
Coefficient reconstruction problem for the~two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 193-213

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

We discuss the inverse problem of successively finding two unknowns (a one-dimensional integral operator kernel and a two-dimensional wave propagation velocity) for the viscoelasticity equation in a weakly horizontally inhomogeneous medium. The direct initial boundary value problem for the displacement function contains zero initial data and the Neumann boundary condition of special form. Additional information consists in the Fourier transform of the displacement function at $x_3=0$. We assume that the unknown functions are expanded in an asymptotic power series in a small parameter. We prove theorems on the global unique solvability and stability of the inverse problem solution.
Keywords: linear viscoelasticity, inverse problem, delta function, stability.
Mots-clés : Fourier transform, kernel, coefficient 
@article{TMF_2022_213_2_a0,
     author = {Zh. D. Totieva},
     title = {Coefficient reconstruction problem for the~two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--213},
     publisher = {mathdoc},
     volume = {213},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a0/}
}
TY  - JOUR
AU  - Zh. D. Totieva
TI  - Coefficient reconstruction problem for the~two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2022
SP  - 193
EP  - 213
VL  - 213
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a0/
LA  - ru
ID  - TMF_2022_213_2_a0
ER  - 
%0 Journal Article
%A Zh. D. Totieva
%T Coefficient reconstruction problem for the~two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2022
%P 193-213
%V 213
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a0/
%G ru
%F TMF_2022_213_2_a0
Zh. D. Totieva. Coefficient reconstruction problem for the~two-dimensional viscoelasticity equation in a weakly horizontally inhomogeneous medium. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 193-213. http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a0/