Controllability of the one-dimensional fractional heat equation under positivity constraints

Biccari U, Warma M, Zuazua E (2020)

Publication Language: English

Publication Type: Journal article

Publication year: 2020

Journal

Communications on Pure and Applied Analysis American Institute of Mathematical Sciences (AIMS)

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)

Involved external institutions

University of Deusto / Universidad de Deusto ES Spain (ES) George Mason University US United States (USA) (US)

How to cite

APA:

Biccari, U., Warma, M., & Zuazua, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Communications on Pure and Applied Analysis, 19(4), 1949-1978. https://dx.doi.org/10.3934/cpaa.2020086

MLA:

Biccari, Umberto, Mahamadi Warma, and Enrique Zuazua. "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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