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.

Keywords

• controllability
• fractional partial differential equation
• linear system
• series solution
• eigenvalue problem