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Carleman Estimates for Second Order Hyperbolic Operators and Applications, a Unified Approach

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Carleman Estimates for Second Order Partial Differential Operators and Applications

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Abstract

In this chapter, we establish three Carleman estimates for second order hyperbolic operators. The first one is Theorem 4.1, which is used to solve an inverse hyperbolic problem. The second one is Theorem 4.2, a Carleman estimate in \(H^1\)-norm, and based on it, we further derive the third Carleman estimate in \(L^2\)-norm (see Theorem 4.3). As the applications of the later, we obtain the exact controllability of semilinear hyperbolic equations and the exponential decay of locally damped hyperbolic equations.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, China

    Xiaoyu Fu, Qi Lü & Xu Zhang

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  1. Xiaoyu Fu
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  2. Qi Lü
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  3. Xu Zhang
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Correspondence to Xiaoyu Fu .

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Fu, X., Lü, Q., Zhang, X. (2019). Carleman Estimates for Second Order Hyperbolic Operators and Applications, a Unified Approach. In: Carleman Estimates for Second Order Partial Differential Operators and Applications. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-29530-1_4

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