Null boundary controllability of a 1-dimensional heat equation with an internal point mass

TL;DR

This paper demonstrates the null boundary controllability of a 1D heat equation system with an internal point mass, using spectral analysis and the moment method to establish controllability with boundary controls.

Contribution

It introduces a novel analysis of a hybrid heat system with an internal mass, proving controllability with boundary controls through spectral and moment method techniques.

Findings

System is null controllable with Dirichlet controls

System is null controllable with Neumann controls

Spectral analysis and moment method are effective for hybrid systems

Abstract

We consider a linear hybrid system composed by two rods of equal length connected by a point mass. We show that the system is null controllable with Dirichlet and Neumann controls. The results are based on a careful spectral spectral analysis together with the moment method.