Email this article Boundary control problem for the telegraph equation
- Authors: Kozlova E.A1
-
Affiliations:
- Samara State Technical University
- Issue: Vol 16, No 2 (2012)
- Pages: 174-177
- Section: Articles
- URL: https://journals.eco-vector.com/1991-8615/article/view/20918
- ID: 20918
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Abstract
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.
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About the authors
Elena A Kozlova
Samara State Technical University
Email: leni2006@mail.ru
аспирант, каф. прикладной математики и информатики; Самарский государственный технический университет; Samara State Technical University
References
- Ильин В. А., Моисеев Е. И. О граничном управлении на одном конце процессом, описываемым телеграфным уравнением // Докл. РАН, 2002. Т. 387, № 5. С. 600-603.
- Ильин В. А., Моисеев Е. И. Граничное управление на двух концах процессом, описываемым телеграфным уравнением // Докл. РАН, 2004. Т. 394, № 2. С. 154-158.
- Бицадзе А. В. Некоторые классы уравнений в частных производных. М.: Наука, 1981. 448 с.
- Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G. Higher transcendental functions. Vol. I / ed. H. Bateman. New York - Toronto - London: McGraw-Hill Book Co, Inc., 1953. 302 pp.;
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