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Control problems governed by a pseudo-parabolic partial differential equation. (English) Zbl 0425.49020


MSC:

49K20 Optimality conditions for problems involving partial differential equations
49J20 Existence theories for optimal control problems involving partial differential equations
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49M29 Numerical methods involving duality
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References:

[1] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. · Zbl 0142.37401
[2] A. G. Butkovskiy, Distributed control systems, Translated from the Russian by Scripta Technica, Inc. Translation Editor: George M. Kranc. Modern Analytic and Computational Methods in Science and Mathematics, No. 11, American Elsevier Publishing Co., Inc., New York, 1969. · Zbl 0197.42204
[3] Robert Wayne Carroll and Ralph E. Showalter, Singular and degenerate Cauchy problems, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Mathematics in Science and Engineering, Vol. 127.
[4] Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. · Zbl 0092.31002
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[6] J.-L. Lions, Optimal control of systems governed by partial differential equations., Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer-Verlag, New York-Berlin, 1971. · Zbl 0203.09001
[7] David G. Luenberger, Optimization by vector space methods, John Wiley & Sons, Inc., New York-London-Sydney, 1969. · Zbl 0176.12701
[8] R. Tyrrell Rockafellar, Convex analysis, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Reprint of the 1970 original; Princeton Paperbacks. · Zbl 0932.90001
[9] D. L. Russell, Controllability and stability theory for linear partial differential equations: Recent progress and open questions, MRC Technical Summary Report #1700, Mathematics Research Center, Madison, Wisconsin, 1976.
[10] R. E. Showalter and T. W. Ting, Pseudo-parabolic partial differential equations, SIAM J. Math. Anal. 1 (1970), 1-26. · Zbl 0199.42102
[11] François Trèves, Basic linear partial differential equations, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 62. · Zbl 0305.35001
[12] L. W. White, Control problems governed by pseudo-parabolic partial differential equations, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1977.
[13] Kôsaku Yosida, Functional analysis, 4th ed., Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 123.
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