Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 26, pp. 1-18.

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

Author: Carole Louis-Rose (Univ. des Antilles, Pointe-a-Pitre, Guadeloupe)

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.
 
Submitted April 5, 2019. Published March 27, 2020.
Math Subject Classifications: 93B05, 35R11, 93C05, 35C10, 93B60.
Key Words: Controllability; fractional partial differential equation;
           linear system; series solution; eigenvalue problem.