Observability of  heat processes by transmutation without geometric restrictions

Sylvain Ervedoza; Enrique Zuazua

doi:10.3934/mcrf.2011.1.177

Article Contents

2011, Volume 1, Issue 2: 177-187. Doi: 10.3934/mcrf.2011.1.177

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Observability of heat processes by transmutation without geometric restrictions

Sylvain Ervedoza^1, and
Enrique Zuazua^2,

1.
CNRS, Institut de Mathématiques de Toulouse, UMR 5219, F-31062 Toulouse
2.
Basque Center for Applied Mathematics (BCAM), Bizkaia Technology Park, Building 500, E-48160 Derio - Basque Country

Received: November 30, 2010

Revised: February 28, 2011

Published: May 2011

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Abstract

The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] and adapted to deal with observability problems) can be applied to derive observability results for the heat equation without any geometric restriction on the subset in which the control is being applied, from a good understanding of the wave equation. Our arguments are based on the recent results in [15] on the frequency depending observability inequalities for waves without geometric restrictions, an iteration argument recently developed in [13] and the new representation formulas in [4] allowing to make a link between heat and wave trajectories.

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Mathematics Subject Classification: Primary: 35C15, 93B07; Secondary: 35K05.

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