Non uniform decay of the energy of some dissipative evolution systems

TL;DR

This paper investigates the energy decay behavior of certain dissipative evolution systems with bounded damping, providing a characterization of non-uniform decay through observability estimates of the undamped system.

Contribution

It introduces a novel characterization of non-uniform energy decay in dissipative systems using observability estimates for the undamped counterpart.

Findings

Established a link between decay rates and observability estimates.

Provided conditions under which energy decay is non-uniform.

Enhanced understanding of damping effects in second order evolution equations.

Abstract

In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.