Skip to main content
SpringerLink
Log in

Optimal control problems for wave equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The problem on minimizing a quadratic functional on trajectories of the wave equation is considered. We assume that the density of external forces is a control function. A control problem for a partial differential equation is reduced to a control problem for a countable system of ordinary differential equations by use of the Fourier method. The controllability problem for this countable system is considered. Conditions of the noncontrollability for some wave equations were obtained.

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. L. D. Akulenko, “Control of the motions of a membrane by means of boundary forces,” Prikl. Mat. Mech., 59, No. 5. 731–741 (1995).

    MathSciNet  Google Scholar 

  2. V. F. Borisov, M. I. Zelikin, and L. A. Manita, “Extremals with accumulation of switchings in an infinite-dimensional space,” J. Math. Sci., 160, No. 2, 139–196 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. G. F. Kuliev, “The problem on pointwise control for a hyperbolic equation,” Avtomat. Telemekh., 80, No. 3, 80–84 (1993).

    MathSciNet  Google Scholar 

  4. J.-L. Lions, “Some questions in the optimal control of distributed systems,” Russ. Math. Surv., 40, No. 4, 57–72 (1985).

    Article  MATH  Google Scholar 

  5. L. A. Manita, “Optimal singular and chattering modes in control problem of oscillating string with fixed ends,” Prikl. Mat. Mekh., 74, No. 5, 873–880 (2010).

    Google Scholar 

  6. M. A. Shubin, Lectures on Equations of Mathematical Physics [in Russian], MCCME, Moscow (2003).

    Google Scholar 

  7. A. G. Sveshnikov, A. N. Bogolubov, and V. V. Kravtsov, Lectures on Mathematical Physics [in Russian], MSU, Moscow (1993).

    Google Scholar 

  8. L. N. Znamenskaya, Control of Elastic Oscillations [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State Institute of Electronics and Mathematics (Technical University), Moscow, Russia

    L. A. Manita

Authors
  1. L. A. Manita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. A. Manita.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 69, Optimal Control, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Manita, L.A. Optimal control problems for wave equations. J Math Sci 177, 257–269 (2011). https://doi.org/10.1007/s10958-011-0456-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-011-0456-x

Keywords

Search

Navigation