Skip to main content
SpringerLink
Log in

High-order asymptotics of a solution of one problem of optimal control over a distributed system with rapidly oscillating coefficients

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

High-order asymptotics is constructed and justified for optimal control over parabolic systems with rapidly oscillating coefficients in the principal part that describes high-intensity heat transfer processes in inhomogeneous and periodic media. The investigation is based on the use of methods of multiscale asymptotic decomposition and some results of the theory of averaging.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodic Media [in Russian] Nauka, Moscow 1984.

    MATH  Google Scholar 

  2. E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory [Russian translation] Mir, Moscow 1984.

    Google Scholar 

  3. J.-L. Lions, Optimal Control of Systems Described by Partial Differential Equations [Russian translation] Mir, Moscow 1972.

    Google Scholar 

  4. V. S. Mel’nik, “Boundary control for nonlinear distributed systems,” Adopt. SAU, Issue 12, 34–42 (1983).

  5. M. I. Khazan, “Boundary-value problems with evolution in the boundary condition,” in: Linear and Nonlinear Problems. Spectral Theory [in Russian], Leningrad University, Leningrad (1986), pp. 105–115.

    Google Scholar 

  6. H. Attouch, “Homogenization,” in: Proceedings of the Bourbaki Seminar, 1988 [Russian translation], Mir, Moscow (1990), pp. 7–31.

    Google Scholar 

  7. V. E. Kapustyan, “Asymptotic analysis of bounded controls in optimal elliptic problems,” Ukr. Mat. Zh., 45, No. 8, 1072–1083 (1993).

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. P. I. Kogut
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kogut, P.I. High-order asymptotics of a solution of one problem of optimal control over a distributed system with rapidly oscillating coefficients. Ukr Math J 48, 1063–1073 (1996). https://doi.org/10.1007/BF02390963

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02390963

Keywords

Search

Navigation