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On the cost of null-control of an artificialadvection-diffusion problem

Published online by Cambridge University Press:  27 August 2013

Pierre Cornilleau  and
Sergio Guerrero
Pierre Cornilleau
Affiliation:
Teacher at Lycée du parc des Loges, 1, boulevard des Champs-Élysées, 91012 Évry, France. [email protected]
Sergio Guerrero
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris Cédex 05, France; [email protected]
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Abstract

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

Keywords

Vanishing viscositycontrollabilityheat equationCarleman
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013 , pp. 1209 - 1224
Copyright
© EDP Sciences, SMAI, 2013

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