Null controllability of a parabolic system with a cubic coupling term

TL;DR

This paper proves that a specific coupled parabolic system with a cubic interaction term can be controlled to reach a null state using localized controls, expanding understanding of controllability in nonlinear PDE systems.

Contribution

It establishes local null controllability for a coupled parabolic system with a cubic coupling term, a novel result in nonlinear control theory.

Findings

System is locally null controllable with localized control.

Cubic coupling term does not prevent controllability.

Advances understanding of control in nonlinear PDE systems.

Abstract

We consider a system of two parabolic equations with a forcing term present in one equation and a cubic coupling term in the other one. We prove that the system is locally null controllable.