Differential Equations

, Volume 45, Issue 6, pp 878–888

Optimal boundary control by an elastic force at one end and a displacement at the other end for an arbitrary sufficiently large time interval in the string vibration problem

  • L. I. Bloshanskaya
  • I. N. Smirnov
Control Theory

DOI: 10.1134/S0012266109060093

Cite this article as:
Bloshanskaya, L.I. & Smirnov, I.N. Diff Equat (2009) 45: 878. doi:10.1134/S0012266109060093


We consider a boundary value problem for the wave equation with given initial conditions and with boundary conditions of the second kind at one end of the string and boundary conditions of the first kind at the other end of the string. We assume the boundary conditions to ensure that the solution of the problem (in the class of generalized functions) satisfying the initial conditions at the initial time t = 0 satisfies given terminal conditions at the terminal time t = T. We clarify the relationship between the functions µ(t) and ν(t) in the boundary conditions and the given functions specifying the initial and terminal states. We obtain closed-form analytic expressions for the functions µ(t) and ν(t) minimizing the boundary energy functional.

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • L. I. Bloshanskaya
    • 1
  • I. N. Smirnov
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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