Quantification of the unique continuation property for the nonstationary Stokes problem

Muriel  Boulakia

doi:10.3934/mcrf.2016.6.27

Article Contents

2016, Volume 6, Issue 1: 27-52. Doi: 10.3934/mcrf.2016.6.27

This issue Previous Article Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation Next Article Optimal sampled-data control, and generalizations on time scales

Quantification of the unique continuation property for the nonstationary Stokes problem

Muriel Boulakia^1,

1.
Sorbonne Universités, UPMC Paris 06, UMR 7598, LJLL, F-75005, Paris

Received: November 30, 2014

Revised: August 31, 2015

Published: February 2016

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Abstract

The purpose of this work is to establish stability estimates for the unique continuation property of the nonstationary Stokes problem. These estimates hold without prescribing boundary conditions and are of logarithmic type. They are obtained thanks to Carleman estimates for parabolic and elliptic equations. Then, these estimates are applied to an inverse problem where we want to identify a Robin coefficient defined on some part of the boundary from measurements available on another part of the boundary.

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Mathematics Subject Classification: 35B35, 35R30, 76D07.

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