Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||21|
|Published online||02 July 2021|
State-constrained controllability of linear reaction-diffusion systems
CEREMADE, Université Paris-Dauphine & CNRS UMR 7534,
* Corresponding author: firstname.lastname@example.org
Accepted: 24 May 2021
We study the controllability of a coupled system of linear parabolic equations, with nonnegativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an “approximate” nonnegativity constraint, and a another stronger one, with “exact” nonnegativity constraint, when all the diffusion coefficients are equal and the eigenvalues of the coupling matrix have nonnegative real part. The proofs are based on a “staircase” method. Finally, we show that state-constrained controllability admits a positive minimal time, even with weaker unilateral constraint on the state.
Mathematics Subject Classification: 35K40 / 35K57 / 93B05 / 93C20
Key words: Control theory / controllability / state-constrained controllability / parabolic equations
© The authors. Published by EDP Sciences, SMAI 2021
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