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

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.

arXiv admin note: text overlap with arXiv:2008.11596, arXiv:2007.08316, arXiv:2012.08219