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

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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 2 1 (Q T ) under minimum requirements on the smoothness of the initial and terminal functions and under natural matching conditions at x = l.