Journal of engineering physics

, Volume 45, Issue 2, pp 940–943 | Cite as

Uniqueness in certain inverse problems of the theory of heat conduction

  • E. V. Bulychev
  • V. B. Glasko


Uniqueness theorems are proved for inverse two-dimensional problems of the theory of heat conduction in two different formulations.


Statistical Physic Heat Conduction Inverse Problem Uniqueness Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Incorrect Problems [in Russian], Nauka, Moscow (1979).Google Scholar
  2. 2.
    O. M. Alifanov, “Regularizing schemes for solving inverse heat-conduction problems,” Inzh.-Fiz. Zh.,24, No. 2, 324–333 (1973).Google Scholar
  3. 3.
    A. N. Tikhonov, N. I. Kulik, I. N. Shklyarov, and V. B. Glasko, “On the results of mathematical modeling of a heat-conducting process,” Inzh.-Fiz. Zh.,39, No. 1, 5–10 (1980).Google Scholar
  4. 4.
    R. Lattes and J.-L. Lions, Method of Quasiinversion and Its Application [Russian translation], Mir, Moscow (1970).Google Scholar
  5. 5.
    N. V. Muzylev, “On the method of quasiinversion,” Zh. Vychisl. Mat. Mat. Fiz.,17, No. 3, 556–561 (1977).Google Scholar
  6. 6.
    é. R. Atamanov, “Uniqueness and estimate of the stability of the solution of a problem for the heat conduction equation with a moving sensor,” Inverse Problems for Differential Equations of Mathematical Physics (ed. by M. M. Lavrent'ev) [in Russian], Izd. Vychisl. Tsentr Sib. Otd. Akad. Nauk SSSR (1978), pp. 35–45.Google Scholar
  7. 7.
    V. B. Glasko and E. E. Kondorskaya, “On the question of constructing Tikhonov regularizing algorithms for one-dimensional inverse heat-conduction problems,” Inzh.-Fiz. Zh.,43, No. 4, 631–637 (1982).Google Scholar
  8. 8.
    A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1966).Google Scholar
  9. 9.
    R. Courant and D. Hilbert, Methods of Mathematical Physics [Russian translation], Vol. 1, GITTL, Leningrad (1951).Google Scholar
  10. 10.
    A. N. Tikhonov and A. G. Sveshnikov, Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1970).Google Scholar
  11. 11.
    V. A. Ditkin and A. P. Prudnikov, Operational Calculus [in Russian], Vysshaya Shkola, Moscow (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • E. V. Bulychev
    • 1
  • V. B. Glasko
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

Personalised recommendations