Null controllability of the linear Stabilized Kuramoto-Sivashinsky system using moment method

TL;DR

This paper establishes the null controllability of a coupled Kuramoto-Sivashinsky and heat system using the moment method, with localized interior and boundary controls, advancing control theory for complex PDE systems.

Contribution

It demonstrates null controllability for a coupled PDE system with a single control, employing the moment method, which is a novel application for this type of system.

Findings

Null controllability achieved with localized interior control.

Null controllability achieved with boundary control.

Application of the moment method to coupled PDEs.

Abstract

This paper deals with the null controllability of a coupled parabolic system, which is Kuramoto-Sivashinsky-Korteweg-de Vries equation coupled with heat equation through first order derivative. More precisely, we prove the null controllability of the system with a single localized bilinear interior control acting on either of the components of the coupled system, and with a single periodic boundary control acting through zeroth order derivatives of either of the components. We employ the well-known moment method to study the controllability of the concerned system.