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Exact controllability theorems for linear parabolic equations in one space dimension

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References

  1. Courant, R., & D. Hilbert, Methods of Mathematical Physics. Vol. I, New York: Interscience Pub. Co. 1953.

    Google Scholar 

  2. Dunford, N., & J. T. Schwartz, Linear Operators. Part II. Spectral Theory. New York: Interscience Pub. Co. 1963.

    Google Scholar 

  3. Egorov, Yu. V., Certain problems in the theory of optimal control. Dokl. Akad. Nauk. SSSR 145, 241–244 (1962). (Russian; English translation in Soviet Mathematics 3, 1080–1084 (1962).)

    Google Scholar 

  4. Egorov, Yu. V., Some problems in the theory of optimal control. Ž. Vyčisl. Mat. Fiz. 5, 887–904 (1963).

    Google Scholar 

  5. Fattorini, H. O., Boundary control systems. SIAM Journal on Control 6, 349–385 (1968).

    Google Scholar 

  6. Fattorini, H. O., Control in finite time of differential equations in Banach space. Comm. Pure Appl. Math. 19, 17–34 (1966).

    Google Scholar 

  7. Friedman, A., Partial Differential Equations of Parabolic Type. Englewood Cliffs, N.J.: Prentice Hall Pub. Co. 1964.

    Google Scholar 

  8. Gal'chuk, L. I., Optimal control of systems described by parabolic equations. Vest. Mosk. Univ., Mat., Mekh. 3, 21–33 (1968). (Russian; English translation in SIAM Journal on Control 7, 546–558 (1969).)

    Google Scholar 

  9. Hille, E., Analytic Function Theory. Vol. II. Boston: Ginn & Co. 1962.

    Google Scholar 

  10. Kaczmarz, S., & H. Steinhaus, Theorie der Orthogonalreihen. Monografje Matematyczne, Tom VI. Warsaw-Lwow 1935.

  11. Ladyzhenskaya, O. A., V. A. Solonnikov & N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type. Izd. “Nauka”, Moscow, 1967. (Russian; English translation, Amer. Math. Soc., Providence, R. I. (1968)).

    Google Scholar 

  12. Müntz, Ch., Über den Approximationssatz von Weierstrass. Math. Abh. (Sch. Festschr.) 303–312 1914.

  13. Paley, R.E.A.C., & N. Wiener, Fourier Transforms in the Complex Domain. Amer. Math. Soc. Colloq. Publ. 19, Providence, R. I. (1934).

  14. Redheffer, R. M., Elementary remarks on completeness. Duke Math. Jour. 35, 103–116 (1968).

    Google Scholar 

  15. Russell, D. L., Nonharmonic Fourier series in the control theory of distributed parameter systems. J. Math. Anal. Appl. 18, 542–560 (1967).

    Google Scholar 

  16. Schwartz, L., Etude des sommes d'exponentielles. Deuxième édition. Paris: Hermann 1959.

    Google Scholar 

  17. Schwartz, L., Théorie des distributions. Paris: Hermann 1950.

    Google Scholar 

  18. Tricomi, F. G., Equazioni differenziali. Einaudi, Torino, 1953 (English translation, Differential Equations. New York: Hafner Pub. Co. 1961.)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles

    H. O. Fattorini & D. L. Russell

  2. Departments of Mathematics and Computer Science, University of Wisconsin, Madison

    H. O. Fattorini & D. L. Russell

Authors
  1. H. O. Fattorini
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  2. D. L. Russell
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Communicated by J. Serrin

This research was supported in part by the National Science Foundation under Contract CP-9658 and by the Office of Naval Research under Contract NR 041-464.

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Fattorini, H.O., Russell, D.L. Exact controllability theorems for linear parabolic equations in one space dimension. Arch. Rational Mech. Anal. 43, 272–292 (1971). https://doi.org/10.1007/BF00250466

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