On the stability of Bresse system with one discontinuous local internal Kelvin-Voigt damping on the axial force

TL;DR

This paper studies the stability of a Bresse system with a discontinuous Kelvin-Voigt damping on the axial force, proving strong stability and polynomial energy decay rates.

Contribution

It introduces a novel analysis of a Bresse system with a discontinuous internal damping, establishing stability and decay properties using advanced mathematical methods.

Findings

System is strongly stable under given conditions.

Energy decays polynomially with specific rates.

Discontinuous damping affects decay behavior.

Abstract

In this paper, we investigate the stabilization of a linear Bresse system with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type acting on the axial force, under fully Dirichlet boundary conditions. First, using a general criteria of Arendt-Batty, we prove the strong stability of our system. Finally, using a frequency domain approach combined with the multiplier method, we prove that the energy of our system decays polynomially with different rates.