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Sibirsk. Mat. Zh., 2005, Volume 46, Number 5, Pages 1053–1071 (Mi smj1021)  

This article is cited in 16 scientific papers (total in 16 papers)

Solvability of the inverse problem of finding thermal conductivity

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study the inverse problem of finding the coefficient of thermal conductivity of the heat equation (along with the solution). As the overdetermination condition we take the values of the solution at the final time. Existence of a regular solution is proven.

Keywords: heat equation in divergent form, problem with unknown thermal conductivity, final overdetermination condition, regular solution

Full text: PDF file (252 kB)
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English version:
Siberian Mathematical Journal, 2005, 46:5, 841–856

Bibliographic databases:

UDC: 516.946, 519.632.8
Received: 11.04.2004

Citation: A. I. Kozhanov, “Solvability of the inverse problem of finding thermal conductivity”, Sibirsk. Mat. Zh., 46:5 (2005), 1053–1071; Siberian Math. J., 46:5 (2005), 841–856

Citation in format AMSBIB
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\by A.~I.~Kozhanov
\paper Solvability of the inverse problem of finding thermal conductivity
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 5
\pages 1053--1071
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\zmath{https://zbmath.org/?q=an:1119.35117}
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\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 5
\pages 841--856
\crossref{https://doi.org/10.1007/s11202-005-0082-2}
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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. V. L. Kamynin, “On the Inverse Problem of Determining the Leading Coefficient in Parabolic Equations”, Math. Notes, 84:1 (2008), 45–54  mathnet  crossref  crossref  mathscinet  isi
    2. Kamynin V.L., Kostin A.B., “Two inverse problems of finding a coefficient in a parabolic equation”, Differ Equ, 46:3 (2010), 375–386  crossref  mathscinet  zmath  isi  elib  scopus
    3. N. V. Beilina, “O razreshimosti obratnoi zadachi dlya giperbolicheskogo uravneniya s integralnym usloviem pereopredeleniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(23) (2011), 34–39  mathnet  crossref
    4. Pan J., “On an Overdetermined Problem of Determining Parameter in a Degenerate Parabolic Equation”, Lith Math J, 51:4 (2011), 533–542  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kamynin V.L., “Unique Solvability of the Inverse Problem of Determination of the Leading Coefficient in a Parabolic Equation”, Differ Equ, 47:1 (2011), 91–101  crossref  mathscinet  mathscinet  zmath  zmath  isi  elib  elib  scopus
    6. Kamynin V.L., “Inverse Problem of Finding the Coefficient of a Lower Derivative in a Parabolic Equation on the Plane”, Differ. Equ., 48:2 (2012), 214–223  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. T. K. Yuldashev, “Obratnaya zadacha dlya nelineinogo uravneniya s psevdoparabolicheskim operatorom vysokogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 17–29  mathnet  crossref  zmath
    8. G. A. Sviridyuk, S. A. Zagrebina, “Neklassicheskie modeli matematicheskoi fiziki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 7–18  mathnet
    9. Aliev Z.S., Mehraliev Ya.T., “An Inverse Boundary Value Problem For a Second-Order Hyperbolic Equation With Nonclassical Boundary Conditions”, Dokl. Math., 90:1 (2014), 513–517  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kamynin V.L., Kostin A.B., “Inverse Problem of Finding N Coefficients of Lower Derivatives in a Parabolic Equation”, Differ. Equ., 50:4 (2014), 476–488  crossref  mathscinet  zmath  isi  elib  scopus
    11. A. B. Kostin, “Recovery of the coefficient of $u_t$ in the heat equation from a condition of nonlocal observation in time”, Comput. Math. Math. Phys., 55:1 (2015), 85–100  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. Kostin A.B., “Inverse Problem With Nonlocal Observation of Finding the Coefficient Multiplying U (T) in the Parabolic Equation”, Differ. Equ., 52:2 (2016), 220–239  crossref  mathscinet  zmath  isi  elib  scopus
    13. Azizbayov E., Mehraliyev Ya., “Solvability of Nonlocal Inverse Boundary-Value Problem For a Second-Order Parabolic Equation With Integral Conditions”, Electron. J. Differ. Equ., 2017, 125  mathscinet  zmath  isi
    14. 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
    15. Dmitriev O.S., Zhivenkova A.A., “Numerical-Analytical Solution of the Nonlinear Coefficient Inverse Heat Conduction Problem”, J. Eng. Phys. Thermophys., 91:6 (2018), 1353–1364  crossref  isi  scopus
    16. Azizbayov E.I., Mehraliyev Ya.T., “Nonlocal Inverse Problem For Determination of Time Derivative Coefficient in a Second-Order Parabolic Equation”, Adv. Differ. Equ. Control Process., 19:1 (2018), 15–36  crossref  isi
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