Stabilization of second-order evolution equations with time delay
Serge Nicaise, Cristina Pignotti
TL;DR
This paper establishes conditions under which second-order evolution equations with damping and time delay are exponentially stable, applying the results to wave, elasticity, and Petrovsky systems.
Contribution
It provides a unified abstract framework for analyzing exponential stability of second-order systems with delay, extending to several physical models.
Findings
Exponential stability conditions derived for abstract second-order systems.
Application of stability results to wave, elasticity, and Petrovsky equations.
Framework facilitates stability analysis in systems with damping and delay.
Abstract
We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity system and the Petrovsky system.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Advanced Mathematical Physics Problems