Minimal time of null controllability of two parabolic equations

Ouaili Lydia

doi:10.3934/mcrf.2019031

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2020, Volume 10, Issue 1: 89-112. Doi: 10.3934/mcrf.2019031

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Minimal time of null controllability of two parabolic equations

Ouaili Lydia^,

Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

^* Corresponding author
^* Corresponding author

Received: April 30, 2018

Revised: November 30, 2018

Early access: April 2019

Published: February 2020

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We consider a one-dimensional 2 × 2 parabolic equations, simultaneously controllable by a localized function in their source term. We also consider a simultaneous boundary control. In each case, we prove the existence of minimal time T₀(q) of null controllability, that is to say, the corresponding problem is null controllable at any time T > T₀(q) and not null controllable for T < T₀(q). We also prove that one can expect any minimal time associated to the boundary control problem.

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Mathematics Subject Classification: Primary: 35K10, 93B05, 34L10.

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