Abstract
For second-order hyperbolic equations with variable coefficient principal part, we establish a global observability-type estimate, whereby the energy of the solutions in L 2(Ω) × H −1(Ω) is bounded by appropriate boundary traces, modulo lower-order terms. This extends the proof and the results of [L-T.2] from the constant coefficient to the variable coefficient case. The pseudo-differential analysis of [L-T.2] is combined with Riemann geometric multipliers [Y.1], which replace the Euclidean multipliers of [L-T.2] in the constant coefficient case.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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© 1999 IFIP International Federation for Information Processing
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Lasiecka, I., Triggiani, R., Yao, PF. (1999). An Observability Estimate in L 2(Ω) × H −1(Ω) for Second-Order Hyperbolic Equations with Variable Coefficients. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_9
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DOI: https://doi.org/10.1007/978-0-387-35359-3_9
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