Geodesic
Boundary Control Problem for the Telegraph Equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 174-177

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In the paper we consider the boundary control problem for the telegraph equation. We study the case of the short period of control, when the initial and final data determine the solution in two regions, having the common part. It means, the control problem has the solution only for the special way related initial and final conditions. We give these relations for two intervals of control time changing and construct solutions for two Cauchy problems in the regions bounded by the characteristics of the equation. This construction allows to find data on characteristics and to solve two Goursat problems. Finally, the substitution of necessary values of spatial coordinate in the obtained expressions gives the required boundary control functions.
Keywords: telegraph equation, boundary control, Riemann method. 
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     author = {E. A. Kozlova},
     title = {Boundary {Control} {Problem} for the {Telegraph} {Equation}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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E. A. Kozlova. Boundary Control Problem for the Telegraph Equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 174-177. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a19/