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

Carole Louis-Rose (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian (−d2 x)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. .

Mots clés: Series solution; Eigenvalue problem; Linear system; Fractional partial differential equation; Controllability

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Carole Louis-Rose. Null controllability from the exterior of fractional parabolic-elliptic coupled systems. Electronic Journal of Differential Equations, 2020, 26, pp.1-18. ⟨hal-02522012⟩