The essential spectrum of advective equations

TL;DR

This paper characterizes the essential spectrum of linear advective PDEs with pseudodifferential perturbations, linking it to the bicharacteristic-amplitude system, and explores implications for stability analysis.

Contribution

It provides a general spectral description for advective PDEs with pseudodifferential perturbations and connects the spectrum to the bicharacteristic-amplitude system.

Findings

Spectral points in the Sacker-Sell spectrum exponentiate into the PDE spectrum.

Exact spectral pictures are derived for various cases.

Applications to instability analysis are demonstrated.

Abstract

A description of the essential spectrum is given for a general class of linear advective PDE with pseudodifferential bounded perturbation. We prove that every point in the Sacker-Sell spectrum of the corresponding bicharacteristic-amplitude system exponentiates into the spectrum of PDE. Exact spectral pictures are found in various cases. Applications to instability are presented.