Stabilization to trajectories for parabolic equations

TL;DR

This paper develops methods for stabilizing semilinear parabolic equations to desired trajectories using finite-dimensional controls supported in small regions, applicable to both internal and boundary control scenarios.

Contribution

It introduces a new stabilization approach for parabolic equations that employs finite-dimensional controls supported locally, extending existing techniques to trajectory stabilization.

Findings

Achieved exponential stabilization to trajectories.

Applicable to both internal and boundary controls.

Controls are supported in small regions.

Abstract

The feedback exponential stabilization to trajectories for semilinear parabolic equations in a given bounded domain is addressed. The controls take values in a finite-dimensional space and are supported in a small region. Both internal and boundary controls are considered.