We consider second-order evolution equations in an abstract setting with intermittently delayed/not-delayed damping and give sufficient conditions ensuring asymptotic and exponential stability results. Our abstract framework is then applied to the wave equation, the elasticity system, and the Petrovsky system. For the Petrovsky system with clamped boundary conditions, we further prove an internal observability estimate that was not available in the literature.
"Asymptotic stability of second-order evolution equations with intermittent delay." Adv. Differential Equations 17 (9/10) 879 - 902, September/October 2012. https://doi.org/10.57262/ade/1355702926