Abstract
Motivated by Fu et al. (SIAM J. Control Optim. 46: 1578–1614, 2007), we present in this paper some ‘algebraic’ conditions that ensure the controllability of wave equations with non-constant coefficients. Compared with the ‘geometric’ conditions obtained in Yao (SIAM J. Control Optim. 37: 1568–1599, 1999), the conditions presented here are easier to be verified because only the first order derivatives of the coefficients are involved.
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References
Bardos, C., Lebeau, G., Rauch, J.: Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary. SIAM J. Control Optim. 30, 1024–1065 (1992)
Fu, X., Yong, J., Zhang, X.: Exact controllability for multidimensional semilinear hyperbolic equations. SIAM J. Control Optim. 46, 1578–1614 (2007)
Yao, P.F.: On the observability inequalities for exact controllability of wave equations with variable coefficients. SIAM J. Control Optim. 37, 1568–1599 (1999)
Yao, P.F.: Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach. Chapman and Hall/CRC Press, Boca Raton (2011)
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The author wants to thank the anonymous reviewers for so many helpful comments to improve this contribution.
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The author was partially supported by the University of Regensburg.
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Liu, Y. Some Sufficient Conditions for the Controllability of Wave Equations with Variable Coefficients. Acta Appl Math 128, 181–191 (2013). https://doi.org/10.1007/s10440-013-9825-4
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DOI: https://doi.org/10.1007/s10440-013-9825-4