Geodesic
Inverse problem for a~system of integro-differential equations for SH waves in a~visco-elastic porous medium: Global solvability
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 491-506

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

We consider a system of hyperbolic integro-differential equations for SH waves in a visco-elastic porous medium. The inverse problem is to recover a kernel (memory) in the integral term of this system. We reduce this problem to solving a system of integral equations for the unknown functions. We apply the principle of contraction mappings to this system in the space of continuous functions with a weight norm. We prove the global unique solvability of the inverse problem and obtain a stability estimate of a solution of the inverse problem.
Keywords: integro-differential equation, inverse problem, Dirac delta function, hyperbolic equation, global solvability, weight function.
Mots-clés : kernel, Lame coefficient 
@article{TMF_2018_195_3_a8,
     author = {D. K. Durdiev and A. A. Rakhmonov},
     title = {Inverse problem for a~system of integro-differential equations for {SH} waves in a~visco-elastic porous medium: {Global} solvability},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {491--506},
     publisher = {mathdoc},
     volume = {195},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a8/}
}
TY  - JOUR
AU  - D. K. Durdiev
AU  - A. A. Rakhmonov
TI  - Inverse problem for a~system of integro-differential equations for SH waves in a~visco-elastic porous medium: Global solvability
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 491
EP  - 506
VL  - 195
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a8/
LA  - ru
ID  - TMF_2018_195_3_a8
ER  - 
%0 Journal Article
%A D. K. Durdiev
%A A. A. Rakhmonov
%T Inverse problem for a~system of integro-differential equations for SH waves in a~visco-elastic porous medium: Global solvability
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 491-506
%V 195
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a8/
%G ru
%F TMF_2018_195_3_a8
D. K. Durdiev; A. A. Rakhmonov. Inverse problem for a~system of integro-differential equations for SH waves in a~visco-elastic porous medium: Global solvability. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 3, pp. 491-506. http://geodesic.mathdoc.fr/item/TMF_2018_195_3_a8/