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Differential Equations

, Volume 51, Issue 5, pp 701–709 | Cite as

On boundary control problems for the Klein–Gordon–Fock equation with an integrable coefficient

  • L. V. KritskovEmail author
Control Theory

Abstract

We consider the process described in the rectangle Q T = [0 ≤ xl] × [0 ≤ tT ] by the equation u tt -u xx -q(x, t)u = 0 with the condition u(l, t) = 0, where the coefficient q(x, t) is only square integrable on Q T . We show that for T = 2l the problem of boundary control of this process by the condition u(0, t) = µ(t) has exactly one solution in the class W 2 1 (Q T ) under minimum requirements on the smoothness of the initial and terminal functions and under natural matching conditions at x = l.

Keywords

Integration Domain Boundary Control Mixed Problem Volterra Equation Exact Controllability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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