Geodesic
On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 9-18

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The paper deals with an inverse problem for a hyperbolic equation of the third order. An inverse problem is posed, which consists in determining an unknown coefficient that depends on time. As additional information for solving the inverse problem, we set the values of the solution to the problem at an interior point, and prove the existence and uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation of a nonlinear system of integral equations of the Volterra type of the second kind and the proof of its solvability.
Keywords: hyperbolic equation, uniqueness
Mots-clés : inverse coefficient problem, existence, Volterra equation. 
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     title = {On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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B. S. Ablabekov; A. K. Goroev. On the definition of a time-dependent lower coefficient in a third-order hyperbolic equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 34 (2021) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/VKAM_2021_34_1_a0/