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

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Abstract

We consider the process described in the rectangle Q T = [0 ≤ x ≤ l] × [0 ≤ t ≤ T ] 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 12 (Q T ) under minimum requirements on the smoothness of the initial and terminal functions and under natural matching conditions at x = l.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    L. V. Kritskov

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  1. L. V. Kritskov
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Correspondence to L. V. Kritskov.

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Original Russian Text © L.V. Kritskov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 5, pp. 688–696.

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Kritskov, L.V. On boundary control problems for the Klein–Gordon–Fock equation with an integrable coefficient. Diff Equat 51, 701–709 (2015). https://doi.org/10.1134/S0012266115050122

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  • DOI: https://doi.org/10.1134/S0012266115050122

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