Nonlinear damping effects for the 2D Mindlin-Timoshenko system

TL;DR

This paper investigates the energy decay in a 2D Mindlin-Timoshenko system with nonlinear damping on rotation angles, proving energy dissipation and decay rates under specific conditions.

Contribution

It provides new results on the asymptotic behavior and explicit decay rates of the system with nonlinear damping, especially when wave speeds are equal.

Findings

Energy decreases over time due to nonlinear dissipation.

Explicit decay rates are established when wave speeds are equal.

Solution existence for the system is confirmed.

Abstract

We study in this article the asymptotic behavior of the Mindlin-Timoshenko system subject to a nonlinear dissipation acting only on the equations of the rotation angles. First, we briefly recall the existence of the solution of this system. Then, we prove that the energy associated with the Mindlin-Timoshenko system fulfills a dissipation relationship showing that the energy is decreasing. Moreover, when the wave speeds are equal, we establish an explicit and general decay result for the energy.