Eventual differentiability of a string with local Kelvin–Voigt damping∗
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
∗∗ Corresponding author: firstname.lastname@example.org
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
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