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Asymptotics for wave equations with Wentzell boundary conditions and boundary damping

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Abstract

We are concerned with linear wave equations with Wentzell boundary conditions of dynamical type, where only one velocity feedback force acts on the Wentzell boundary. By using the theory of strongly continuous semigroups of linear operators, we prove that the energies of the solutions are strongly stable. Moreover, we show in the one dimensional case that there are solutions decaying at arbitrarily slow rates.

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Acknowledgments

The authors would like to thank the referee very much for his/her helpful suggestions. The work was supported partly by the NSF of China (11371095, 11271082), the Shanghai Key Laboratory for Contemporary Applied Mathematics (08DZ2271900), and the Laboratory of Nonlinear Mathematical Modeling and Methods (Ministry of Education).

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  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Chan Li & Ti-Jun Xiao

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  1. Chan Li
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  2. Ti-Jun Xiao
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Correspondence to Ti-Jun Xiao.

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Communicated by Abdelaziz Rhandi.

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Li, C., Xiao, TJ. Asymptotics for wave equations with Wentzell boundary conditions and boundary damping. Semigroup Forum 94, 520–531 (2017). https://doi.org/10.1007/s00233-016-9779-8

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  • DOI: https://doi.org/10.1007/s00233-016-9779-8

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