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Kuznetsov, Yu. A.

Necessary conditions for optimality in problems of control by systems described by elliptic equations. (English) Zbl 0437.49024

Sib. Math. J. 20, 410-417 (1980).
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Cited in 2 Documents

MSC:

49K20 Optimality conditions for problems involving partial differential equations
93C20 Control/observation systems governed by partial differential equations
35J40 Boundary value problems for higher-order elliptic equations

Citations:

Zbl 0417.49026
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References:

[1] V. I. Plotnikov, ?Necessary and sufficient conditions for optimality and uniqueness conditions for optimizing functions for general control systems,? Izv. Akad. Nauk SSSR, Ser. Mat.,36, No. 3, 652-679 (1972).
[2] A. I. Egorov, ?A variational problem in the theory of elliptic equations,? Sib. Mat. Zh.,5, No. 3, 500-508 (1964). · Zbl 0124.05401
[3] J. L. Lions, ?Sur le contrôle optimal de systémes decrits per des équations aux dériveés partielles linéaires. Equations elliptiques,? Sci. C. R., Acad. Paris,263, No. 20, 713-715 (1966). · Zbl 0148.07801
[4] U. E. Raitum, ?Some extremal problems connected with linear elliptic equations,? Latv. Mat. Ezhegodnik,4, 257-279 (1968).
[5] E. I. Nenakhov and V. N. Gorchakov, ?Necessary conditions on the extremum in problems of optimal control of systems described by elliptic equations in partial derivatives,? Kibernetika, No. 2, 77-80 (1972). · Zbl 0235.49022
[6] T. Zolezzi, ?Necessary conditions for optimal controls of elliptic or parabolic problems,? SIAM J. Control,10, No. 4, 594-607 (1972). · Zbl 0278.49024 · doi:10.1137/0310044
[7] V. N. Gorchakov, ?A problem in optimal control of a system described by an elliptic differential equation,? Kibernetika, No. 3, 101-103 (1974). · Zbl 0287.49018
[8] I. K. Gogodze, ?Necessary conditions for optimality in elliptic problems of control with integral bounds,? Soobshch. Akad. Nauk GSSR,81, No. 1, 17-20 (1976). · Zbl 0331.49017
[9] O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
[10] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966). · Zbl 0148.12601
[11] G. I. Marchuk, Methods in Computational Mathematics [in Russian], Nauka, Novosibirsk (1973).
[12] A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations [in Russian], Nauka, Moscow (1976).
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