Influence of the hidden regularity on the stability of partially damped systems of wave equations

Approximate internal controllability and synchronization of a coupled system of wave equations

“…The effectiveness of the indirect damping depends in a very complex way on all of the involved factors such as the nature of the coupling term, the order of dissipation, the hidden regularity of undamped equations, the accordance of boundary conditions and many others. We refer [8,28] and the reference therein for the recent progress.…”

Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems

“…It can be served to establish the decay rate, for example, the uniform decay rate as in [22]: 13) where M and ω are positive constants, or the polynomial decay rate for the smooth initial data: 14) where the constant δ > 0 is independent of the initial data. We refer to [7,27] and the references therein for the recent progress on the polynomial stability of indirectly damped wave equations.…”

Stability of piezoelectric beams with magnetic effects of fractional derivative type and with/without thermal effects

“…Then, the polynomial stability of the system will be given by using a result of Borichev and Tomilov. Many scholars have used different methods to analyze the polynomial stability of some other systems, see [1,2,4,9,15,19,21,23,24,26,32]. Finally, for the asymptotic behavior analysis part of system (1.8)-(1.10), we obtain the exponential stability of the system by using perturbed functional method.…”