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Method of inverse dynamical systems for the reconstruction of internal sources and boundary conditions in heat transfer

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Abstract

A method for the inversion of linear dynamical systems is described; it can be used to investigate several inverse problems in the reconstruction of boundary conditions or internal sources in linear transfer equations.

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Literature cited

  1. A. N. Tikhonov and V. S. Arsenin, Solutions of Ill-Posed Problems, Halsted Press, New York (1977).

    Google Scholar 

  2. E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Am. Math. Soc., Providence, RI (1957).

    Google Scholar 

  3. M. M. Lavrent'ev, V. G. Romanov, and S. P. Shishatskii, Some Improperly Posed Problems of Mathematical Physics, Springer-Verlag, Berlin (1967).

    Google Scholar 

  4. V. G. Romanov, Inverse Problems of Mathematical Physics [in Russian], Moscow (1984).

  5. A. L. Bukhgeim, Volterra Equations and Inverse Problems [in Russian], Novosibirsk (1983).

  6. V. T. Borukhov, Avtomat. Telemekh., No. 5, 29–36 (1982).

    Google Scholar 

  7. V. T. Borukhov and P. M. Kolesnikov, Izv. Akad. Nauk SSSR Tekh. Kibern., No. 3, 168–174 (1983).

    Google Scholar 

  8. V. T. Borukhov and P. M. Kolesnikov, Application of the Method of Inverse Dynamical Systems for the Reconstruction of Internal Heat Sources, Preprint Inst. Heat Mass Transfer Acad. Sci. B. SSR No. 11 [in Russian], ITMO AN B. SSR, Minsk (1986).

    Google Scholar 

  9. V. T. Borukhov and L. E. Borisevich, in: Mathematical Models, Analytical and Numerical Methods in Transfer Theory, Proc. Int. School [in Russian], Part 2, Minsk (1986), pp. 124–132 (collected scientific papers, ITMO AN B. SSR).

  10. M. D. Mesarovic and Y. Takahara, General Systems Theory: Mathematical Foundations, Academic Press, New York (1975).

    Google Scholar 

  11. V. T. Borukhov, in: Mathematical Models of Transfer Theory in Inhomogeneous and Nonlinear Media with Phase Transitions [in Russian], Minsk (1986), pp. 46–61 (collected scientific papers, ITMO AN B. SSR).

  12. S. N. Singh, IEEE Trans. Automat. Control,AC-27, No. 1, 276–279 (1982).

    Google Scholar 

  13. A. G. Butkovskii, Characteristics of Distributed-Parameter Systems [in Russian], Moscow (1979).

  14. V. E. Lyantse and O. G. Storozh, Methods of the Theory of Unbounded Operators [in Russian], Kiev (1983).

  15. A. V. Lykov and Yu. A. Mikhailov, Theory of Heat and Mass Transfer [in Russian], Moscow (1963).

  16. A. A. Samarskii, Differents. Uravn.,16, No. 11, 1925–1935 (1980).

    Google Scholar 

  17. A. M. Nakhushev, Differents. Uravn.,19, No. 1, 86–93 (1983).

    Google Scholar 

  18. P. M. Kolesnikov, Methods of Transfer Theory in Nonlinear Media [in Russian], Minsk (1981).

  19. P. M. Kolesnikov, Int. J. Heat Mass Transfer,30, No. 1, 85–92 (1987).

    Google Scholar 

  20. V. A. Steklov, Fundamental Problems of Mathematical Physics [in Russian], Parts 1 and 2, Petrograd (1923).

  21. A. N. Tikhonov, Mat. Sb.,26, No. 1, 35–56 (1950).

    Google Scholar 

  22. Yu. K. Lando, Differents. Uravn.,14, No. 11, 545–548 (1971).

    Google Scholar 

  23. L. I. Kamynin, Zh. Vychisl. Mat. Mat. Fiz.,16, No. 6, 1480–1488 (1976).

    Google Scholar 

  24. N. I. Yurchuk, Differents. Uravn.,22, No. 12, 2117–2126 (1986).

    Google Scholar 

  25. W. Feller, Ann. Math.,55, 468–519 (1952).

    Google Scholar 

  26. A. D. Venttsel', Teor. Veroyatn. Prim.,47, No. 2, 172–185(1959).

    Google Scholar 

  27. V. T. Borukhov, Inzh.-Fiz. Zh.,47, No. 3, 469–474 (1984).

    Google Scholar 

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 2, pp. 304–311, August, 1988.

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Kolesnikov, P.M., Borukhov, V.T. & Borisevich, L.E. Method of inverse dynamical systems for the reconstruction of internal sources and boundary conditions in heat transfer. Journal of Engineering Physics 55, 934–940 (1988). https://doi.org/10.1007/BF00870746

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  • DOI: https://doi.org/10.1007/BF00870746

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