The impact of delay on second-order evolution equations

Abstract

This article aims to exhibit new instability results on the effects of arbitrary delay on a class of second-order evolution equations involving in a Hilbert space. More precisely, we prove that arbitrary finite, large or small delay might remarkably destroy the stability of a well-behaved (stable) system, that is by driving the resulting system with delay to generate non-trivial periodic solutions with constant energy, solutions with exponential growth rate and solutions with blow-up energy. Also, an interesting new effect of large delay is constructively established. We further supply this study with applications and numerical simulations.

Keywords

• second-order evolution equations
• delay effects
• feedback stabilization
• 37l15
• 37l05
• 93b52
• 93b05
• 37n35