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Hyperbolic Equation with Rapidly Oscillating Data: Reconstruction of the Small Lowest Order Coefficient and the Right-Hand Side from Partial Asymptotics of the Solution

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Abstract

We consider the Cauchy problem for a one-dimensional hyperbolic equation. The lowest order coefficient and the right-hand side oscillate in time at a high frequency, and the amplitude of the lowest order coefficient is small. The way of reconstructing these oscillating functions from partial solution asymptotics given at a certain point of the domain is studied.

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REFERENCES

  1. V. G. Romanov, Inverse Problems of Mathematical Physics (Nauka, Moscow, 1984; VNU Science, Utrecht, 1987).

  2. A. M. Denisov, Introduction to the Theory of Inverse Problems (Mosk. Gos. Univ., Moscow, 1994) [in Russian].

    Google Scholar 

  3. S. I. Kabanikhin, Inverse and Ill-Posed Problems: Theory and Applications (Inst. Mat., Novosibirsk, 2009; De Gruyter, Berlin, 2011).

  4. A. O. Vatul’yan, Coefficient Inverse Problems in Mechanics (Fizmatlit, Moscow, 2019) [in Russian].

    Google Scholar 

  5. P. V. Babich and V. B. Levenshtam, “Reconstruction of a rapidly oscillating right-hand side of the wave equation from partial asymptotics of the solution,” Vladikavkaz. Mat. Zh. 22 (4), 28–44 (2020).

    MATH  Google Scholar 

  6. V. B. Levenshtam, “Parabolic equations with large parameter: Inverse problems,” Math. Notes 107 (3), 452–463 (2020).

    Article  MathSciNet  MATH  Google Scholar 

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Funding

The main result of this work (Theorem 2) was obtained under the support of the Russian Science Foundation, project no. 20-11-20141.

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Authors and Affiliations

  1. Southern Federal University, 344090, Rostov-on-Don, Russia

    V. B. Levenshtam

  2. Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    V. B. Levenshtam

Authors
  1. V. B. Levenshtam
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Correspondence to V. B. Levenshtam.

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The author declares that he has no conflicts of interest.

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Translated by I. Ruzanova

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Levenshtam, V.B. Hyperbolic Equation with Rapidly Oscillating Data: Reconstruction of the Small Lowest Order Coefficient and the Right-Hand Side from Partial Asymptotics of the Solution. Dokl. Math. 105, 28–30 (2022). https://doi.org/10.1134/S1064562422010082

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  • DOI: https://doi.org/10.1134/S1064562422010082

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