Geodesic
Eventual differentiability of a string with local Kelvin–Voigt damping
Liu, Kangsheng1  ; Liu, Zhuangyi2  ; Zhang, Qiong3, 4
1 Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R. China.
2 Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, USA.
3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China.
4 Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P.R. China
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 443-454

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In this paper, we study a wave equation with local Kelvin–Voigt damping, which models one-dimensional wave propagation through two segments consisting of an elastic and a viscoelastic medium. Under the assumption that the damping coefficients change smoothly near the interface, we prove that the semigroup corresponding to the system is eventually differentiable.

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DOI : 10.1051/cocv/2015055
Classification : 35M20, 35Q72, 74D05
Keywords: Semigroup, local Kelvin–Voigt damping, eventual differentiability of semigroup

Liu, Kangsheng 1 ; Liu, Zhuangyi 2 ; Zhang, Qiong 3, 4

1 Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R. China.
2 Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812-2496, USA.
3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China.
4 Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P.R. China 
@article{COCV_2017__23_2_443_0,
     author = {Liu, Kangsheng and Liu, Zhuangyi and Zhang, Qiong},
     title = {Eventual differentiability of a string with local {Kelvin{\textendash}Voigt} damping},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {443--454},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {2},
     year = {2017},
     doi = {10.1051/cocv/2015055},
     zbl = {1362.35195},
     mrnumber = {3608088},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015055/}
}
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Liu, Kangsheng; Liu, Zhuangyi; Zhang, Qiong. Eventual differentiability of a string with local Kelvin–Voigt damping. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 443-454. doi: 10.1051/cocv/2015055

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