Null controllability from the exterior of fractional parabolic-elliptic coupled systems

Abstract

We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian \((-d_x^2)^s\), \(s\in(0,1)\), in one space dimension. In each system, the control is located on a non-empty open set of \(\mathbb{R}\setminus(0,1)\). Using the spectral theory of the fractional Laplacian and a unique continuation principle for the dual equation, we show that the problem is null controllable if and only if 1/2<s<1. For more information see https://ejde.math.txstate.edu/Volumes/2020/26/abstr.html