Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix

TL;DR

This paper investigates the null controllability of certain degenerate parabolic PDE systems with non-diagonalizable diffusion matrices, establishing an algebraic criterion based on Kalman's rank condition.

Contribution

It provides a novel algebraic characterization of null controllability for non-diagonalizable degenerate parabolic systems using Kalman's rank condition.

Findings

Null controllability characterized by Kalman's rank condition.

Applicable to systems with constant diffusion, coupling, and control matrices.

Extends controllability theory to non-diagonalizable degenerate PDE systems.

Abstract

In this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are constant and we characterize the null controllability by an algebraic condition so called \textit{Kalman's rank} condition.