Dynamics of thermoelastic plate system with terms concentrated in the boundary: the lower semicontinuity of the global attractors

TL;DR

This paper investigates how the long-term behavior of thermoelastic plate systems with boundary-concentrated reaction terms changes as the boundary neighborhood shrinks, proving the lower semicontinuity of their global attractors.

Contribution

It establishes the lower semicontinuity of global attractors for thermoelastic plates with boundary-concentrated reaction terms as the neighborhood shrinks to the boundary.

Findings

Global attractors are lower semicontinuous with respect to boundary neighborhood shrinking.

Reaction terms concentrated near the boundary influence the system's long-term dynamics.

The results extend understanding of boundary effects on thermoelastic systems.

Abstract

In this paper we show the lower semicontinuity of the global attractors of autonomous thermoelastic plate systems with Neumann boundary conditions when some reaction terms are concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary as a parameter $\varepsilon$ goes to zero.