External boundary regional controllability for nonlocal diffusion systems involving the fractional Laplacian. Issue 2 (2020) - Ge, Fudong; Chen, YangQuan
Abstract: The goal of this paper is to investigate regional exact controllability from the exterior of the nonlocal diffusion system governed by parabolic partial differential equations (PDEs) with the fractional Laplacian. For this purpose, we first explore an explicit expression of solutions to the system. Use this, some equivalent conditions to achieve regional exact controllability of the considered systems are given. Then, we propose an approach on the minimum energy control problem using the Hilbert uniqueness method (HUM). It is presented that the minimum control input can be explicitly given with respect to the subregion, the actuators structure and the spectral theory of fractional Laplacian under zero Dirichlet exterior boundary conditions. An example is finally included to illustrate our theoretical results.