Controllability and observabiliy of an artificial advection-diffusion problem

TL;DR

This paper investigates the controllability and observability of a one-dimensional artificial advection-diffusion system, providing Carleman estimates and analyzing properties like backward uniqueness and control cost behavior as viscosity vanishes.

Contribution

The paper introduces new Carleman estimates for boundary controllability and explores fundamental properties of the system, including backward uniqueness and control cost insights.

Findings

Establishment of boundary observability via Carleman estimates

Demonstration of backward uniqueness for the system

Analysis of control cost behavior as viscosity approaches zero

Abstract

In this paper we study the controllability of an artificial advection-diffusion system through the boundary. Suitable Carleman estimates give us the observability on the adjoint system in the one dimensional case. We also study some basic properties of our problem such as backward uniqueness and we get an intuitive result on the control cost for vanishing viscosity.