Geodesic
2D kernel identification problem in viscoelasticity equation with a weakly horizontal homogeneity
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 1, pp. 14-38

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We consider the problem of determining the kernel $k(t,x)$, $t\in [0,T]$, $x\in {\Bbb R}$, entering the equation of viscoelasticity in a bounded domain with respect to $z$ with weakly horizontal homogeneity. It is assumed that this kernel weakly depends on the variable $x$ and decomposes into a power series by degrees of the small parameter $\varepsilon$. A method for finding unknown functions $k_{0}$, $k_{1}$ is constructed. The global uniquely solvability and stability theorems are obtained.
Keywords: viscoelasticity equation, inverse problem, delta-function, integral equation, Banach theorem. . 
@article{SJIM_2022_25_1_a1,
     author = {D. K. Durdiev and J. Sh. Safarov},
     title = {2D kernel identification problem in viscoelasticity equation with a weakly horizontal homogeneity},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {14--38},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a1/}
}
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D. K. Durdiev; J. Sh. Safarov. 2D kernel identification problem in viscoelasticity equation with a weakly horizontal homogeneity. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 1, pp. 14-38. http://geodesic.mathdoc.fr/item/SJIM_2022_25_1_a1/