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Formulas of boundary control of an inhomogeneous string: I

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References

  1. Belishev, M.I., Mat. Sb., 1989, vol. 189, no. 5, pp. 584–602.

    Google Scholar 

  2. Avdonin, S.A., Belishev, M.I., and Ivanov, S.A., Mat. Sb., 1991, vol. 182, no. 3, pp. 307–331.

    MATH  Google Scholar 

  3. Belishev, M.I. and Glasman, A.K., Algebra i Analiz, 2000, vol. 12, no. 2, pp. 131–187.

    MathSciNet  Google Scholar 

  4. Russell, D.L., SIAM J. Control, 1971, vol. 9, no. 1, pp. 29–42.

    Article  MATH  MathSciNet  Google Scholar 

  5. Russell, D.L., SIAM Rev., 1978, vol. 20, no. 4, pp. 639–739.

    Article  MATH  MathSciNet  Google Scholar 

  6. Tataru, D., Comm. Partial Differential Equations, 1995, vol. 20, no. 5–6, pp. 855–884.

    MATH  MathSciNet  Google Scholar 

  7. Butkovskii, A.G., Metody upravleniya sistemami s raspredelennymi parametrami (Methods for Control of Systems with Distributed Parameters), Moscow: Nauka, 1975.

    Google Scholar 

  8. Komornik, V., Exact Controllability and Stabilization. The Multiplier Method, Paris: Masson, 1994.

    MATH  Google Scholar 

  9. Il’in, V.A., Differ. Uravn., 2000, vol. 36, no. 11, pp. 1513–1528.

    MathSciNet  Google Scholar 

  10. Il’in, V.A., Tr. Mat. Inst. Steklova, 2001, vol. 232, pp. 144–155.

    Google Scholar 

  11. Il’in, V.A. and Moiseev, E.I., Dokl. Akad. Nauk, 2003, vol. 393, no. 6, pp. 730–734.

    MathSciNet  Google Scholar 

  12. Il’in, V.A. and Moiseev, E.I., Dokl. Akad. Nauk, 2004, vol. 394, no. 2, pp. 154–158.

    MathSciNet  Google Scholar 

  13. Borovskikh, A.V., Differ. Uravn., 2002, vol. 38, no. 6, pp. 758–767.

    MathSciNet  Google Scholar 

  14. Borovskikh, A.V., Tr. Semin. im. I.G. Petrovskogo, 2004, vol. 24, pp. 3–43.

    Google Scholar 

  15. Weston, V.H., J. Math. Phys., 1972, vol. 13, no. 12, pp. 1952–1956.

    Article  MATH  MathSciNet  Google Scholar 

  16. Davison, M.E., J. Math. Anal. Appl., 1994, vol. 188, no. 1, pp. 158–181.

    Article  MATH  MathSciNet  Google Scholar 

  17. He, S. An Explicit Time-Domain Solution for the Reflection from a Stratified Acoustic Half-Space Obtained by the Boundary Control Method, Preprint, Royal Institute of Technology, Sweden.

  18. Marchenko, V.A., Spektral’naya teoriya operatorov Shturma-Liuvillya (Spectral Theory of Sturm-Liouville Operators), Kiev: Naukova Dumka, 1972.

    Google Scholar 

  19. Yurko, V.A., Obratnye spektral’nye zadachi i ikh prilozheniya (Inverse Spectral Problems and Their Applications), Saratov: Izdat. Saratovskogo Pedinstituta, 2001.

    Google Scholar 

  20. Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1977.

    Google Scholar 

  21. Levin, V.I. and Grosberg, Yu.I., Differentsial’nye uravneniya matematicheskoi fiziki (Differential Equations of Mathematical Physics), Moscow: GTTI, 1951.

    Google Scholar 

  22. Cinquini-Cibrario, M. and Cinquini, S., Equazioni a derivate parziali di tipo iperbolico, Roma: Edizioni Cremonese, 1964.

    MATH  Google Scholar 

  23. Bitsadze, A.V., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1982.

    Google Scholar 

  24. Friedlander, F.G., Proc. Cambridge Philos. Soc., 1947, vol. 43, no. 3, pp. 348–359.

    Article  MATH  MathSciNet  Google Scholar 

  25. Nakhushev, A.M., Uravneniya matematicheskoi biologii (Equations of Mathematical Biology), Moscow: Vysshaya Shkola, 1995.

    Google Scholar 

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Original Russian Text © A.V. Borovskikh, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 1, pp. 64–89.

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Borovskikh, A.V. Formulas of boundary control of an inhomogeneous string: I. Diff Equat 43, 69–95 (2007). https://doi.org/10.1134/S0012266107010090

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  • DOI: https://doi.org/10.1134/S0012266107010090

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