Spectra of the Gurtin-Pipkin type equations

TL;DR

This paper analyzes the spectral properties of Gurtin-Pipkin type integro-differential equations, focusing on the non-real spectrum under specific kernel conditions, which is important for understanding their stability and dynamics.

Contribution

It provides a detailed description of the non-real spectrum of these equations based on kernel conditions, advancing theoretical understanding of their spectral behavior.

Findings

Characterization of the non-real spectrum under certain kernel conditions

Identification of spectral regions related to stability

Extension of spectral analysis techniques to integro-differential equations

Abstract

We study the spectra of certain integro-differential equations arising in applications. Under some conditions on the kernel of the integral operator, we describe the non-real part of the spectrum.