Controllability of the one-dimensional fractional heat equation under positivity constraints
Biccari U, Warma M, Zuazua Iriondo E (2020)
Publication Language: English
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 19
Pages Range: 1949-1978
Journal Issue: 4
DOI: 10.3934/cpaa.2020086
Abstract
In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian (-d(x)(2))(s) (0 < s < 1) on the interval (-1, 1). We prove the existence of a minimal (strictly positive) time T-min such that the fractional heat dynamics can be controlled from any initial datum in L-2 (-1, 1) to a positive trajectory through the action of a positive control, when s > 1/2. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical results.
Authors with CRIS profile
Enrique Zuazua Iriondo
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Additional Organisation(s)
Involved external institutions
University of Deusto / Universidad de Deusto
Spain (ES)
George Mason University
United States (USA) (US)
Spain (ES)
George Mason University
United States (USA) (US)
How to cite
APA:
Biccari, U., Warma, M., & Zuazua Iriondo, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Communications on Pure and Applied Analysis, 19(4), 1949-1978. https://doi.org/10.3934/cpaa.2020086
MLA:
Biccari, Umberto, Mahamadi Warma, and Enrique Zuazua Iriondo. "Controllability of the one-dimensional fractional heat equation under positivity constraints." Communications on Pure and Applied Analysis 19.4 (2020): 1949-1978.
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