Abstract
For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented.
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Bardos, C., Lebeau G., Rauch, J., Un example d’utilisation des notions de propagation pour le contrôle et la stabilisation des problèmes hyperboliques, Rend. Sem. Mat. Univ. Pol. Torino, 1988, Spec. Issue (1989): 11–31.
Lagnese, J., Control of wave processes with distributed controls supported on a subregion, SIAM Journal of Control and Optimization, 1983, 21: 68–85.
Liu, K., Locally distributed control and damping for the conservative systems, SIAM Journal of Control and Optimization, 1997, 35: 1574–1590.
Wu, H., Shen, L. L. Yu, Y. L., Introduction to Riemannian Geometry (in Chinese), Beijing: Peking University Press, 1989.
Yao, P. F., On the observability inequality for exact controllability of wave equations with variable coefficients, SIAM Journal of Control and Optimization, 1999, 37: 1568–1599.
Grisvard, P., Elliptic Problems in Nonsmooth Domain, Monographs Studies Math. 24, Boston: Pitman, 1985.
Komornik, V., Exact Controllability and Stabilization, Research in Applied Mathematics (eds. Ciarlet, P. G., Lions, J.), Paris, New York: Masson/John Wiley Copublication, 1994.
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Feng, S., Feng, D. Locally distributed control of wave equations with variable coefficients. Sci China Ser F 44, 309–315 (2001). https://doi.org/10.1007/BF02714718
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DOI: https://doi.org/10.1007/BF02714718