For the inhomogeneous telegraph equation with a variable coefficient in the rectangle [0, l] x[0, T], we study the following problem of control of its solution u(x, t): bring the solution from a given state {u(x, 0), ut(x, 0)} to a given final state {u(x, T), ut(x, T)} using the boundary control by an elastic force mu(t) = ux(0, t) on the left end of the interval [0, l] with the right end being fixed (u(l, t) = 0). We prove that for T = 2l the desired boundary control exists and is unique for the broadest classes of initial and final functions. The solution is constructed using a Neumann series whose convergence is implied by an estimate for the kernel of its integral operator.
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