Inverse Ingham type inequalities for the Burgers model

TL;DR

This paper establishes inverse Ingham type inequalities for the Burgers model, a fundamental step in understanding the reachability and control properties of viscoelastic systems with both elastic and viscous characteristics.

Contribution

It introduces inverse Ingham inequalities for the Burgers model, advancing the analysis of controllability in viscoelasticity by examining eigenvalue gaps and Fourier series representations.

Findings

Proves inverse Ingham inequalities for the Burgers model

Demonstrates a reachability theorem for the system

Analyzes eigenvalue gaps and Fourier solutions

Abstract

Viscoelastic materials have the properties both of elasticity and viscosity. In a previous work we investigate glass relaxation in the framework of viscoelasticity. Here we consider the Burgers model, a first but meaningful step in the general analysis, showing a reachability theorem thanks the analysis of the gap between eigenvalues and the representation of the solution in Fourier series.