Polynomial Stability of an Elastic Thin Plate on Non-Smooth Domain

TL;DR

This paper investigates polynomial stabilization of an elastic thin plate on non-smooth domains, addressing boundary singularities and demonstrating stability under specific geometric conditions and control strategies.

Contribution

It establishes polynomial decay rates for elastic plates on domains with small corners and introduces corner feedback control to recover stability in larger corner angles.

Findings

Polynomial decay is achieved on domains with small corner angles.

Boundary singularities affect solution regularity and stability.

Corner feedback control restores polynomial stability for larger angles.

Abstract

This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem as a precise variational framework. We prove that for domains with sufficiently small corner angles, the system retains the polynomial decay rate under standard geometric control conditions. In cases where larger corner angles lead to a significant regularity loss, we show that polynomial stability is recovered by introducing a feedback control at the corners.