Geodesic
Boundary Control Problem for the Telegraph Equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 127 (2012) no. 2, pp. 174-177 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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E. A. Kozlova. Boundary Control Problem for the Telegraph Equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 127 (2012) no. 2, pp. 174-177. http://geodesic.mathdoc.fr/item/VSGTU_2012_127_2_a19/

[1] Il'in V. A., Moiseev E. I., “Boundary control at one endpoint of a process described by a telegraph equation”, Dokl. Akad. Nauk, 387:5 (2002), 600–603 | MR | Zbl

[2] Il'in V. A., Moiseev E. I., “Boundary control at two endpoints of a process described by the telegraph equation”, Dokl. Akad. Nauk, 394:2 (2004), 154–158 | MR | Zbl

[3] Bitsadze A. V., “Some classes of partial differential equations”, Moscow, 1981, 448 pp. | MR | Zbl

[4] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher transcendental functions, v. I, ed. H. Bateman, McGraw-Hill Book Co, Inc., New York – Toronto – London, 1953, 302 pp. ; Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. V 3-kh t., v. 1, Gipergeometricheskaya funktsiya. Funktsiya Lezhandra, Nauka, M., 1973, 296 pp. | Zbl