Rate of decay of some Petrowsky-like dissipative systems

TL;DR

This paper investigates the decay rates of Petrowsky-like dissipative systems, establishing that the fastest decay is determined by the spectral properties of the system's generator under certain conditions.

Contribution

It provides a spectral characterization of the maximal decay rate for specific dissipative systems, extending understanding of their stability behavior.

Findings

Fastest decay rate equals the supremum of the real part of the spectrum.

Spectral gap condition is crucial for the decay rate characterization.

Applications demonstrate the theoretical results in practical settings.

Abstract

In this paper, we show that the fastest decay rate for some Petrowsky-like dissipative systems is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the corresponding operator satisfied some spectral gap condition. We give also some applications to illustrate our setting.