# On the cost of null-control of an artificial advection-diffusion problem

Pierre Cornilleau; Sergio Guerrero

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 4, page 1209-1224
- ISSN: 1292-8119

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topCornilleau, Pierre, and Guerrero, Sergio. "On the cost of null-control of an artificial advection-diffusion problem." ESAIM: Control, Optimisation and Calculus of Variations 19.4 (2013): 1209-1224. <http://eudml.org/doc/272842>.

@article{Cornilleau2013,

abstract = {In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.},

author = {Cornilleau, Pierre, Guerrero, Sergio},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {vanishing viscosity; controllability; heat equation; Carleman; Carleman estimate},

language = {eng},

number = {4},

pages = {1209-1224},

publisher = {EDP-Sciences},

title = {On the cost of null-control of an artificial advection-diffusion problem},

url = {http://eudml.org/doc/272842},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Cornilleau, Pierre

AU - Guerrero, Sergio

TI - On the cost of null-control of an artificial advection-diffusion problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 4

SP - 1209

EP - 1224

AB - In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.

LA - eng

KW - vanishing viscosity; controllability; heat equation; Carleman; Carleman estimate

UR - http://eudml.org/doc/272842

ER -

## References

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