Stability and instability results of the Kirchhoff plate equation with delay terms on boundary or dynamical boundary controls

TL;DR

This paper investigates the stability properties of the Kirchhoff plate equation with boundary delay controls, providing conditions for stability and instability, and establishing well-posedness and stability results.

Contribution

It introduces new stability analysis for the Kirchhoff plate equation with boundary delays, including instability examples and stability conditions without geometric constraints.

Findings

Identified conditions leading to instability with boundary delays.

Proved well-posedness of the delayed Kirchhoff plate system.

Established strong and exponential stability under specific conditions.

Abstract

In this paper, we consider the Kirchhoff plate equation with delay terms on the boundary control are added (see system \eqref{p5-2.1} below). we give some instability examples of system \eqref{p5-2.1} for some choices of delays. Finally, we prove its well-posedness, strong stability without any geometric condition and exponential stability under a multiplier geometric control condition.