Open AccessEventual differentiability of coupled wave equations with local Kelvin-Voigt damping
Author(s) -
Ahmed Bchatnia,
Nadia Souayeh
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022098
Subject(s) - dissipative system , semigroup , differentiable function , physics , work (physics) , differential equation , wave equation , mathematical analysis , mathematics , quantum mechanics
In this work, we consider a coupled wave equations with partially and locally distributed Kelvin-Voigt damping, where only one equation is dissipative. Under the assumption that the damping coefficient changes smoothly near the interface of the damped and undamped regions, we investigate the effectiveness of the indirect control, and we prove that the associated semigroup is eventually differential.