On the existence of optimal controls of the first boundary value problems for parabolic partial delay-differential equations in divergence form

S. NABABAN; K. L. TEO

doi:10.2969/jmsj/03220343

S. NABABAN, K. L. TEO

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1980 年 32 巻 2 号 p. 343-362

DOI https://doi.org/10.2969/jmsj/03220343

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Published: 1980 Received: 1978/07/13 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) N. U. Ahmed and K. L. Teo, An existence theorem on optimal control of partially observable diffusions, SIAMJ. Control, 12 (1974), 351-355.
2) W.H. Fleming, Optimal control of partially observable diffusions, SIAM J. Control, 6 (1968), 194-214.
3) J. L. Lions, Optimal Controls of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
4) E. S. Noussair, S. Nababan and K. L. Teo, On the existence of optimal controls for quasi-linear parabolic partial differential equations, J. Optimization theory Appl., to appear.
5) T. Zolezzi, Teoremi d'esistenza per problemi di controllo ottimo retti da equazioni ellittiche or paraboliche, Rend. Sem. Mat. Univ. Padova, 44 (1970), 155-173.
6) K. L. Teo and N. U. Ahmed, On the optimal controls of a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions, Ann. Mat. Pura Appl., to appear.
7) D. G. Aronson, Nonnegative solutions of linear parabolic equations, Ann. Scuola Nonm. Sup. Pisa, 22 (1968), 607-694.
8) E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1965.
9) S. Nababan and K. L. Teo, On the system governed by parabolic partial delayequations with first boundary conditions, Ann. Mat. Pura Appl., to appear.
10) C. J. Himmelberg, M. Q. Jacobs and F. S. von Vleck, Measurable multifunctions, selectors, and Filippov's implicit functions lemma, J. Math. Anal. Appl., 25 (1969), 276-284.
11) L. D. Berkovitz, A lower closure theorem for abstract control problems with L_p-bounded controls, J. Optimization Theory Appl., 14 (1974), 521-528.

Right : [1] N. U. Ahmed and K. L. Teo, An existence theorem on optimal control of partially observable diffusions, SIAMJ. Control, 12 (1974), 351-355.
[2] W. H. Fleming, Optimal control of partially observable diffusions, SIAM J. Control, 6 (1968), 194-214.
[3] J. L. Lions, Optimal Controls of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
[4] E. S. Noussair, S. Nababan and K. L. Teo, On the existence of optimal controls for quasi-linear parabolic partial differential equations, J. Optimization theory Appl., to appear.
[5] T. Zolezzi, Teoremi d'esistenza per problemi di controllo ottimo retti da equazioni ellittiche or paraboliche, Rend. Sem. Mat. Univ. Padova, 44 (1970), 155-173.
[6] K. L. Teo and N. U. Ahmed, On the optimal controls of a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions, Ann. Mat. Pura Appl., to appear.
[7] D. G. Aronson, Nonnegative solutions of linear parabolic equations, Ann. Scuola Nonm. Sup. Pisa, 22 (1968), 607-694.
[8] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1965.
[9] S. Nababan and K. L. Teo, On the system governed by parabolic partial delayequations with first boundary conditions, Ann. Mat. Pura Appl., to appear.
[10] C. J. Himmelberg, M. Q. Jacobs and F. S. von Vleck, Measurable multifunctions, selectors, and Filippov's implicit functions lemma, J. Math. Anal. Appl., 25 (1969), 276-284.
[11] L. D. Berkovitz, A lower closure theorem for abstract control problems with L_p-bounded controls, J. Optimization Theory Appl., 14 (1974), 521-528.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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