Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability

Thuy N. T. Nguyen

doi:10.3934/mcrf.2014.4.203

Article Contents

2014, Volume 4, Issue 2: 203-259. Doi: 10.3934/mcrf.2014.4.203

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Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability

Thuy N. T. Nguyen^1,

1.
Université d'Orléans, Bâtiment de Mathématiques (MAPMO), B.P. 6759, 45067 Orléans cedex 2

Received: January 2013

Revised: July 2013

Published: June 2014

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Abstract

In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator $\partial_t-\partial_x (c\partial_x )$ where the diffusion coefficient $c$ has a jump. As a consequence of this Carleman estimate, we deduce consistent null-controllability results for classes of semi-linear parabolic equations.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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