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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 5, Pages 744–752 (Mi zvmmf9855)  

This article is cited in 6 scientific papers (total in 6 papers)

Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative

A. M. Denisov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation.

Key words: inverse problem, hyperbolic equation, small parameter, parabolic equation, asymptotic expansion.

DOI: https://doi.org/10.7868/S0044466913050049

Full text: PDF file (194 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:5, 580–587

Bibliographic databases:

UDC: 519.633.9
Received: 06.12.2012

Citation: A. M. Denisov, “Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 744–752; Comput. Math. Math. Phys., 53:5 (2013), 580–587

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. V. Babich, V. B. Levenshtam, “Direct and inverse asymptotic problems with high-frequency terms”, Asymptotic Anal., 97:3-4 (2016), 329–336  crossref  mathscinet  zmath  isi  elib  scopus
    2. P. V. Babich, V. B. Levenshtam, S. P. Prika, “Recovery of a rapidly oscillating source in the heat equation from solution asymptotics”, Comput. Math. Math. Phys., 57:12 (2017), 1908–1918  mathnet  crossref  crossref  isi  elib
    3. A. M. Denisov, S. I. Solov'eva, “Numerical solution of inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative”, Differ. Equ., 54:7 (2018), 900–910  crossref  isi  scopus
    4. P. V. Babich, V. B. Levenshtam, “Recovery of a Rapidly Oscillating Absolute Term in the Multidimensional Hyperbolic Equation”, Math. Notes, 104:4 (2018), 489–497  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. B. Levenshtam, “Parabolic Equations with Large Parameter. Inverse Problems”, Math. Notes, 107:3 (2020), 452–463  mathnet  crossref  crossref  mathscinet  isi  elib
    6. P. V. Babich, V. B. Levenshtam, “Vosstanovlenie bystro ostsilliruyuschei pravoi chasti volnovogo uravneniya po chastichnoi asimptotike resheniya”, Vladikavk. matem. zhurn., 22:4 (2020), 28–44  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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