Null-controllability of linear hyperbolic systems in one dimensional space

TL;DR

This paper proves null-controllability of linear hyperbolic systems in one dimension for any time greater than the optimal, under boundary control and generic assumptions, extending previous results to all source terms.

Contribution

It establishes null-controllability for all source terms and any time beyond the optimal, generalizing prior work that was limited to generic source terms.

Findings

Null-controllability achieved for any time > optimal time

Results hold for all source terms

Discussion of exact controllability similar to null-controllability

Abstract

This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously established the optimal time for the null and the exact controllability for this system for a generic source term. In this work, we prove the null-controllability for any time greater than the optimal time and for any source term. Similar results for the exact controllability are also discussed.