A unique continuation result for the plate equation and an application

TL;DR

This paper establishes a unique continuation property for the plate equation with non-smooth coefficients and applies it to analyze the global attractor in a damped semilinear setting.

Contribution

It introduces a novel unique continuation result for weak solutions of the plate equation with irregular coefficients and demonstrates its application to the study of global attractors.

Findings

Proved unique continuation for weak solutions with non-smooth coefficients.

Applied the result to analyze the global attractor for a damped semilinear plate equation.

Enhanced understanding of the long-term behavior of solutions in damped plate systems.

Abstract

In this paper, we prove the unique continuation property for the weak solution of the plate equation with non-smooth coefficients. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping.