Null controllability of an ODE-heat system with coupled boundary and internal terms

TL;DR

This paper investigates the null controllability of a coupled ODE-heat system with boundary and internal controls, providing theoretical proofs via Carleman estimates and numerical validation.

Contribution

It introduces a novel approach combining Carleman estimates and domain extension to establish controllability for coupled ODE-heat systems.

Findings

Null controllability achieved for the coupled system.

Numerical experiments confirm theoretical results.

Method applicable to systems with boundary and internal controls.

Abstract

This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the ODE-heat with distributed control using Carleman estimates. Then, we conclude by the strategy of space domain extension. Finally, we illustrate the analysis with some numerical experiments.