Controllability of shadow reaction-diffusion systems

Hernández-Santamaría V, Zuazua Iriondo E (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Journal of Differential Equations Elsevier

DOI: 10.1016/j.jde.2019.10.012

Abstract

We study the null controllability of linear shadow models for reaction-diffusion systems arising as singular limits when the diffusivity of some of the components is very high. This leads to a coupled system where one component solves a parabolic partial differential equation (PDE) and the other one an ordinary differential equation (ODE). We analyze these shadow systems from a controllability perspective and prove two types of results. First, by employing Carleman inequalities and ODE arguments, we prove that the null controllability of the shadow model holds. This result, together with the effectiveness of the controls to control the original dynamics, is illustrated by numerical simulations. We also obtain a uniform Carleman estimate for the reaction-diffusion equations which allows to obtain the null control for the shadow system as a limit when the diffusivity tends to infinity in one of the equations.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Hernández-Santamaría, V., & Zuazua Iriondo, E. (2019). Controllability of shadow reaction-diffusion systems. Journal of Differential Equations. https://doi.org/10.1016/j.jde.2019.10.012

MLA:

Hernández-Santamaría, Víctor, and Enrique Zuazua Iriondo. "Controllability of shadow reaction-diffusion systems." Journal of Differential Equations (2019).

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