Study of the cost of the controllability of second order parabolic equations with a small diffusion and a transport term - Archive ouverte HAL
Preprints, Working Papers, ... Year : 2020

Study of the cost of the controllability of second order parabolic equations with a small diffusion and a transport term

Jon Asier Bárcena-Petisco
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Abstract

In this paper we consider the heat equation with Neumann, Robin and mixed boundary conditions (with coefficients on the boundary which depend on the space variable). The main results concern the behaviour of the cost of the null controllability with respect to the diffusion coefficient when the control acts in the interior. First, we prove that if we almost have Dirichlet boundary conditions in the part of the boundary in which the flux of the transport enters, the cost of the controllability decays for a time $T$ sufficiently large. Next, we show some examples of Neumann and mixed boundary conditions in which for any time T>0 the cost explodes exponentially as the diffusion coefficient vanishes. Finally, we study the cost of the problem with Neumann boundary conditions when the control is localized in the whole domain.
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Dates and versions

hal-02455632 , version 1 (26-01-2020)
hal-02455632 , version 2 (27-02-2020)
hal-02455632 , version 3 (09-11-2020)
hal-02455632 , version 4 (05-04-2021)
hal-02455632 , version 5 (26-11-2021)

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  • HAL Id : hal-02455632 , version 2

Cite

Jon Asier Bárcena-Petisco. Study of the cost of the controllability of second order parabolic equations with a small diffusion and a transport term. 2020. ⟨hal-02455632v2⟩
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