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**Inverse problems in the multidimensional hyperbolic equation with rapidly oscillating absolute term.**
*(English)*
Zbl 1478.35030

Kusraev, Anatoly G. (ed.) et al., Operator theory and differential equations. Selected papers based on the presentations at the 15th conference on order analysis and related problems of mathematical modeling, Vladikavkaz, Russia, July 15–20, 2019. Cham: Birkhäuser. Trends Math., 7-23 (2021).

Summary: The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are imposed only on several first terms of the asymptotics of the solution rather than on the whole solution. This approach is realized in the case of a multidimensional hyperbolic equation with unknown absolute term.

For the entire collection see [Zbl 1470.47003].

For the entire collection see [Zbl 1470.47003].

### MSC:

35B40 | Asymptotic behavior of solutions to PDEs |

35R30 | Inverse problems for PDEs |

35L20 | Initial-boundary value problems for second-order hyperbolic equations |

34C29 | Averaging method for ordinary differential equations |

### Keywords:

multidimensional hyperbolic equation; rapidly oscillating absolute term; asymptotics of solution
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\textit{P. V. Babich} and \textit{V. B. Levenshtam}, in: Operator theory and differential equations. Selected papers based on the presentations at the 15th conference on order analysis and related problems of mathematical modeling, Vladikavkaz, Russia, July 15--20, 2019. Cham: Birkhäuser. 7--23 (2021; Zbl 1478.35030)

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