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A positional control problem for a nonlinear parabolic system

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References

  1. Krasovskii, N.N.,Igrovye zadachi o vstreche dvizhenii (Game Problems on the Encounter of Motions), Moscow, 1971.

  2. Krasovskii, N.N. and Subbotin, A.I.,Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow, 1974.

  3. Krasovskii, N.N.,Upravlenie dinamicheskoi sistemoi (Control of Dynamical System), Moscow, 1985.

  4. Osipov, Yu.S.,Dokl. Akad. Nauk SSSR, 1971, vol. 196, no. 4, pp. 779–782.

    MathSciNet  Google Scholar 

  5. Osipov, Yu.S.,Prikl. Mat. Mekh., 1971, vol. 35, no. 1, pp. 123–131.

    MathSciNet  Google Scholar 

  6. Osipov, Yu.S. and Okhezin, S.P.,Dokl. Akad. Nauk SSSR, 1976, vol. 226, no. 6, pp. 1314–1317.

    Google Scholar 

  7. Korotkii, A.I. and Osipov, Yu.S.,Prikl. Mat. Mekh., 1980, vol. 44, no. 4, pp. 611–617.

    MathSciNet  Google Scholar 

  8. Maksimov, V.I.,Differents. Uravn., 1992, vol. 28, no. 6, pp. 961–967.

    MathSciNet  Google Scholar 

  9. Osipov, Yu.S. and Kryazhimskii, A.V.,Inverse Problems of Ordinary Differential Equations: Dynamical Solution, Gordon and Breach, 1995.

  10. Osipov, Yu.S., Kryazhimskii, A.V., and Maksimov, V.I.,Zadachi dinamicheskoi regulyarizatsii dlyasistem s raspredelennymi parametrami (Dynamic Regularization Problems for Systems with Distributed Parameters), Sverdlovsk, 1991.

  11. Maksimov, V.I.,Differents. Uravn., 1990, vol. 26, no. 12, pp. 2059–2067; 1991, vol. 27, no. 4, pp. 567–573.

    MATH  MathSciNet  Google Scholar 

  12. Osipov, Yu.S., Kryazhimskii, A.V., and Maksimov, V.I.,J. Inv. Ill-Posed Problems, 1996, vol. 4, no. 4, pp. 267–282.

    Article  MATH  MathSciNet  Google Scholar 

  13. Caginalp, G.,Arch. Rat. Mech. Analysis, 1986, vol. 92, pp. 205–245.

    Article  MATH  MathSciNet  Google Scholar 

  14. Hoffman, K.-H. and Jiang, L.S.,Numer. Fund. Anal, and Optimiz., 1992, vol. 13, no. 1–2, pp. 11–27.

    Article  Google Scholar 

  15. Chen, Z., Das Phasenfeldmodell für das Problem der Phasenübergange,Dissertation, Universität Augsburg, 1992.

  16. Neittaanmaki, P. and Tiba, D.,Optimal Control of Nonlinear Parabolic Systems, New York, 1994.

  17. Lions, J.-L.,Optimal Control of Systems Governed by Partial Differential Equations, Berlin a.o., 1971. Translated under the titleOptimal’noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymiproizvodnymi, Moscow: Mir, 1972.

  18. Lions, J.-L. and Magenes, E.,Problèmes aux limites non homogénes et applications, Paris: Dunod, 1968. Translated under the titleNeodnorodnye granichnye zadachi i ikh prilozheniya, Moscow: Mir, 1971.

    MATH  Google Scholar 

  19. Lions, J.-L.,Controle des systèmes distribues singuliers, Paris: Gauthier-Villars, 1983. Translated under the titleUpravlenie singulyarnymi raspredelennymi sistemami, Moscow: Mir, 1987.

    MATH  Google Scholar 

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Maksimov, V.I. A positional control problem for a nonlinear parabolic system. Diff Equat 36, 1202–1210 (2000). https://doi.org/10.1007/BF02754188

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