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 (-d2x)s, s ∈ (0, 1), in one space dimension. In each system, the control is located on a non-empty open set of ℝ / (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.