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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 779–792 (Mi zvmmf10032)  

This article is cited in 10 scientific papers (total in 10 papers)

Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations

A. B. Kostin

National Research Nuclear University УMEPhIФ, Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: Examples of inverse problems of source reconstruction with nonunique solutions are constructed. Problems for parabolic, elliptic, and hyperbolic equations are considered. Additional data (overdetermination) is specified as a final observation condition.

Key words: counterexamples, inverse problems, final observation, parabolic, elliptic, and hyperbolic equations.

DOI: https://doi.org/10.7868/S0044466914020100

Full text: PDF file (276 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 779–792

Bibliographic databases:

UDC: 519.632.8
Received: 14.07.2013

Citation: A. B. Kostin, “Counterexamples in inverse problems for parabolic, elliptic, and hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 779–792; Comput. Math. Math. Phys., 54:5 (2014), 779–792

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Tabarintseva, “On approximate solution of non-linear inverse problem”, 2017 2Nd International Ural Conference on Measurements, URALCON 2017, IEEE, 99–106  crossref  isi
    2. I. Orazov, M. A. Sadybekov, “On an inverse problem of mathematical modeling of the extraction process of polydisperse porous materials”, Advancements in mathematical sciences (ams 2015), AIP Conf. Proc., 1676, eds. A. Ashyralyev, E. Malkowsky, A. Lukashov, F. Basar, Amer. Inst. Phys., 2015, UNSP 020005  crossref  isi  scopus
    3. I. Orazov, M. A. Sadybekov, “One-dimensional diffusion problem with not strengthened regular boundary conditions”, 41st international conference applications of mathematics in engineering and economics (amee'15), AIP Conf. Proc., 1690, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2015, UNSP 040007  crossref  isi  scopus
    4. N. E. Erzhanov, I. Orazov, “On one mathematical model of the extraction process of polydisperse porous material”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 5–15  mathnet  crossref  elib
    5. A. I. Prilepko, A. B. Kostin, V. V. Solovev, “Obratnye zadachi nakhozhdeniya istochnika i koeffitsientov dlya ellipticheskikh i parabolicheskikh uravnenii v prostranstvakh Geldera i Soboleva”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 67–85  mathnet  crossref
    6. A. B. Kostin, “Carleman parabola and the eigenvalues of elliptic operators”, Differ. Equ., 54:3 (2018), 318–329  crossref  mathscinet  zmath  isi  scopus
    7. M. A. Sadybekov, G. Dildabek, M. B. Ivanova, “On an inverse problem of reconstructing a heat conduction process from nonlocal data”, Adv. Math. Phys., 2018, 8301656  crossref  mathscinet  isi  scopus
    8. B. Aibek, A. Aimakhanova, G. Besbaev, M. A. Sadybekov, “About one inverse problem of time fractional evolution with an involution perturbation”, International Conference on Analysis and Applied Mathematics (ICAAM 2018), AIP Conf. Proc., 1997, eds. A. Ashyralyev, A. Lukashov, M. Sadybekov, Amer. Inst. Phys., 2018, 020012-1  crossref  isi  scopus
    9. A. S. Erdogan, D. Kusmangazinova, I. Orazov, M. A. Sadybekov, “On one problem for restoring the density of sources of the fractional heat conductivity process with respect to initial and final temperatures”, Bull. Karaganda Univ-Math., 91:3 (2018), 31–44  crossref  isi
    10. Kirane M., Sadybekov M.A., Sarsenbi A.A., “On An Inverse Problem of Reconstructing a Subdiffusion Process From Nonlocal Data”, Math. Meth. Appl. Sci., 42:6 (2019), 2043–2052  crossref  isi  scopus
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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