| Issue |
ESAIM: COCV
Volume 23, Number 2, April-June 2017
|
|
|---|---|---|
| Page(s) | 443 - 454 | |
| DOI | https://doi.org/10.1051/cocv/2015055 | |
| Published online | 17 January 2017 | |
Eventual differentiability of a string with local Kelvin–Voigt damping∗
1 Department of Mathematics, Zhejiang University, Hangzhou
310027, P.R. China.
ksliu@zju.edu
2 Department of Mathematics and Statistics, University of
Minnesota, Duluth, MN 55812-2496, USA.
zliu@d.umn.edu
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
∗∗ Corresponding author: zhangqiong@bit.edu.cn
Received:
16
September
2014
Revised:
29
August
2015
Accepted:
11
December
2015
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.
Mathematics Subject Classification: 35M20 / 35Q72 / 74D05
Key words: Semigroup / local Kelvin–Voigt damping / eventual differentiability of semigroup
© EDP Sciences, SMAI 2017
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