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Mat. Zametki, 2018, Volume 104, Issue 4, Pages 505–515 (Mi mz12151)  

Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation

P. V. Babicha, V. B. Levenshtamab

a Southern Federal University, Rostov-on-Don
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

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

Keywords: multidimensional hyperbolic equation, rapidly oscillating absolute term, asymptotics of solution, inverse problem.

DOI: https://doi.org/10.4213/mzm12151

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English version:
Mathematical Notes, 2018, 104:4, 489–497

Bibliographic databases:

UDC: 517.955.8
Received: 29.11.2017

Citation: P. V. Babich, V. B. Levenshtam, “Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation”, Mat. Zametki, 104:4 (2018), 505–515; Math. Notes, 104:4 (2018), 489–497

Citation in format AMSBIB
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\pages 505--515
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