Asymptotic stability of intermittently damped semi-linear hyperbolic-type equations

Abstract

<p style='text-indent:20px;'>Of concern is asymptotic stability for second order semilinear evolution equations in a Hilbert space with intermittent damping. We obtain asymptotic stability results, without the assumption that the damping coefficient <inline-formula><tex-math id="M1">\begin{document}$ a(t) $\end{document}</tex-math></inline-formula> is always positive, which means that the unique damping term could vanish sometimes. Moreover, we do not need the condition that the main linear operator <inline-formula><tex-math id="M2">\begin{document}$ A $\end{document}</tex-math></inline-formula> is coercive, that is, <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula> could have a non-trivial kernel.</p>