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Equivalence between internal observability and exponential stabilization for suspension bridge problem

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Abstract

We study the fourth order semilinear suspension bridge problem with restoring force h(u) and linear damping \(\delta u_{t}\). Using the multiplier method, we first establish the observability inequality of the corresponding system without damping term. Then we show an equivalence between observability and exponential stabilization of this system by using an appropriate decomposition technique and the semigroup method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant number 11771216], the Key Research and Development Program of Jiangsu Province (Social Development) [Grant number BE2019725], the Six Talent Peaks Project in Jiangsu Province [Grant number 2015-XCL-020] and the Qing Lan Project of Jiangsu Province.

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  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Yasi Zheng, Wenjun Liu & Yadong Liu

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  1. Yasi Zheng
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  2. Wenjun Liu
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  3. Yadong Liu
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Correspondence to Wenjun Liu.

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Zheng, Y., Liu, W. & Liu, Y. Equivalence between internal observability and exponential stabilization for suspension bridge problem. Ricerche mat 71, 711–721 (2022). https://doi.org/10.1007/s11587-021-00566-4

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