The problem of determining the memory of an environment with weak horizontal heterogeneity
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 3, pp. 383-402
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The problem of determining the convolutional kernel $k(t,x)$, $t>0$, $x \in {\mathbb{R}}$, included in a hyperbolic integro-differential equation of the second order, is investigated in a domain bounded by a variable $z$ and having weakly horizontal heterogeneity. It is assumed that this kernel weakly depends on the variable $x$ and decomposes into a power series by degrees of a small parameter $\varepsilon$. A method for finding the first two coefficients $k_{0}(t)$, $k_{1}(t)$ of this expansion is constructed according to the given first two moments in the variable $x$ of the solution of the direct problem at $z=0$.
Keywords:
integro-differential equation, inverse problem, the Dirac delta function, the kernel of the integral, the norm.
@article{VUU_2022_32_3_a2,
author = {D. K. Durdiev and J. Sh. Safarov},
title = {The problem of determining the memory of an environment with weak horizontal heterogeneity},
journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
pages = {383--402},
publisher = {mathdoc},
volume = {32},
number = {3},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_3_a2/}
}
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D. K. Durdiev; J. Sh. Safarov. The problem of determining the memory of an environment with weak horizontal heterogeneity. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 3, pp. 383-402. http://geodesic.mathdoc.fr/item/VUU_2022_32_3_a2/