Controllability of cascade coupled systems of multi-dimensional evolution PDE's by a reduced number of controls

TL;DR

This paper establishes controllability results for cascade-coupled systems of multi-dimensional evolution PDEs using fewer controls, with applications to hyperbolic, parabolic, and diffusive equations.

Contribution

It introduces new controllability results for cascade-coupled PDE systems with a reduced number of boundary or local controls, applicable to various types of equations.

Findings

Controllability achieved with fewer controls in cascade systems

Applicable to hyperbolic, parabolic, and diffusive PDEs

Provides theoretical foundation for control reduction strategies

Abstract

We prove controllability results for abstract systems of weakly coupled $N$ evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N-1$ controls. We give applications to cascade coupled systems of $N$ multi-dimensional-hyperbolic, parabolic and diffusive equations.