Skip to main content
SpringerLink
Log in

Optimal control of one-dimensional linear parabolic differential equations

  • Conference paper
  • First Online:
Optimization and Optimal Control

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 477))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bieberbach, L. Einführung in die Theorie der Differentialgleichungen im reellen Gebiet. Springer Verlag, Berlin-Göttingen-Heidelberg, 1956.

    MATH  Google Scholar 

  • Butkovskiy, A. G. Distributed control systems, Elsevier, New Y., 1969.

    MATH  Google Scholar 

  • Butkovskiy, A. G., A. Egorov and K. Lurie Optimal control of distributed parameter systems/A survey of Soviet publications, SIAM J. Control, Vol. 6, pp. 437–476, 1968.

    Article  MathSciNet  Google Scholar 

  • Demyanov, V. F. and A. M. Rubinov Approximate methods in optimization problems. American Elsevier Publishing Comp., Inc., New York, 1970.

    Google Scholar 

  • Fattorini, H. O. Time optimal control of solutions of operational differential equations. SIAM J. Control, Ser. A, 2, pp. 54–59, 1964.

    MathSciNet  MATH  Google Scholar 

  • Fattorini, H. O. Boundary control systems. SIAM J. Control, Vol. 6, pp. 349–385, 1968.

    Article  MathSciNet  MATH  Google Scholar 

  • Glashoff, K. and S. A. Gustafson Numerical treatment of a parabolic boundary-value control problem, to appear in J. Optimization Theory and Applications, 1975.

    Google Scholar 

  • Glashoff, K. and W. Krabs Dualität und Bang-Bang-Prinzip bei einem parabolischen Rand-Kontrollproblem. To appear in ‘Bonner Mathem. Schriften', 1975.

    Google Scholar 

  • Köthe, G. Topologische lineare Räume I, Springer Verlag, Berlin-Heidelberg-New York, 1966.

    MATH  Google Scholar 

  • Lions, J. J. Contrôle Optimale de Systèmes Gouvernés par des Équations aux Dérivées partielles, Dunod, Paris, 1968.

    Google Scholar 

  • Mikhlin, S. G. The numerical performance of variational methods, Wolters-Nordhoff Publishing Company, Groningen, The Netherlands, 1971.

    MATH  Google Scholar 

  • Pschenitschny, B. N. Notwendige Optimalitätsbedingungen, R. Oldenbourg Verlag, München-Wien, 1972.

    MATH  Google Scholar 

  • Robinson, A. C. A survey of optimal control of distributed—parameter systems, Automatica, Vol. 7, pp. 371–388, 1971.

    Article  MATH  Google Scholar 

  • Tsujioka, K. Remarks on controllability of second order evolution equations in Hilbert spaces, SIAM J. Control, Vol. 8 No. 1, 1970.

    Google Scholar 

  • Weck, N. Über das Prinzip der eindeutigen analytischen Fortsetzbarkeit in der Kontrolltheorie, this volume, 1975.

    Google Scholar 

  • Yegorov, Yu. V. Some problems in the theory of optimal control, USSR Comp. Math. Vol. 3, No. 5, 1963.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TH Darmstadt Fachbereich Mathematik, Schloßgartenstr. 7, D-61, Darmstadt, W.-Germany

    Klaus Glashoff

Authors
  1. Klaus Glashoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technischen Universität München, 8 München, Postfach 202420, BRD

    Roland Bulirsch

  2. Fakultät für Mathematik und Informatik, Universität Mannheim, 68 Mannheim, Schloß, BRD

    Werner Oettli

  3. Institut für Angewandte Mathematik und Statistik der Universität Würzburg, 87 Würzburg, Am Hubland, BRD

    Josef Stoer

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Glashoff, K. (1975). Optimal control of one-dimensional linear parabolic differential equations. In: Bulirsch, R., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Mathematics, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079170

Download citation

  • DOI: https://doi.org/10.1007/BFb0079170

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07393-2

  • Online ISBN: 978-3-540-37591-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation