Electron. J. Differential Equations, Vol. 2020 (2020), No. 26, pp. 1-18.

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

Carole Louis-Rose

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.

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Carole Louis-Rose
Université des Antilles
Département de Mathématiques et Informatique
laboratoire LAMIA, campus de Fouillole
97157 Pointe-à-Pitre, Guadeloupe
email: carole.louis-rose@univ-antilles.fr

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