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Optimal control of systems governed by elliptic operator of infinite order

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 964))

Abstract

In the present paper, using the theory of J.L. Lions [6,7] we find the set of inequalities defining an optimal control of systems governed by elliptic operator of infinite order. The questions treated in this paper are related to a previous result by I.M. Gali; et al. [5], but in different direction, by taking the case of operators of infinite order with finite dimension.

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References

  1. Ju.A. Dubinskii, Sobolev spaces of infinite order and the behavior of solutions of some boundary value problem with unbounded increase of the order of the equation. Math. USSR Sb. 27 (1975) 143–162.

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  5. I.M. Gali and H.A. El-Saify, Optimal control of systems governed by a self-adjoint elliptic operator with an infinite number of variables. International Conference Functional-Differential Systems and Related Topics II, 3–10 May 1981 Poland.

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  6. J.L. Lions, Optimal control of systems governed by partial differential equations, Springer-Verlag Band 170 (1971).

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  7. J.L. Lions and E. Magenes, Non-homogeneous boundary value problem and applications, Springer-Verlag, Vol. III (1972).

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Author notes

  1. I. M. Gali

    Present address: Department of Mathematics, Qatar University, P.O. Box 2713, Doha

Authors and Affiliations

    Authors
    1. I. M. Gali
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    Editor information

    W.N. Everitt B.D. Sleeman

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    © 1982 Springer-Verlag

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    Gali, I.M. (1982). Optimal control of systems governed by elliptic operator of infinite order. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065003

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    • DOI: https://doi.org/10.1007/BFb0065003

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-11968-5

    • Online ISBN: 978-3-540-39561-4

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