Geodesic
Inverse boundary-value problem for a pseudoparabolic-pseudohyperbolic integro-differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 16-32

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In this paper, we examine the solvability of a nonlocal inverse boundary-value problem for a mixed pseudoparabolic-pseudohyperbolic integro-differential equation with spectral parameters. Regular and irregular values of the spectral parameters are found. For regular values of spectral parameters, we obtain a criterion for the unique solvability of the inverse boundary-value problem. For irregular values of spectral parameters, we establish a criterion for the existence of an infinite set of solutions.
Keywords: integro-differential equation, mixed-type equation, spectral parameter, integral condition, solvability. 
@article{INTO_2021_201_a1,
     author = {T. K. Yuldashev (Iuldashev) and B. I. Islomov},
     title = {Inverse boundary-value problem for a pseudoparabolic-pseudohyperbolic integro-differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {16--32},
     publisher = {mathdoc},
     volume = {201},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_201_a1/}
}
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T. K. Yuldashev (Iuldashev); B. I. Islomov. Inverse boundary-value problem for a pseudoparabolic-pseudohyperbolic integro-differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 16-32. http://geodesic.mathdoc.fr/item/INTO_2021_201_a1/