Observability of heat processes by transmutation without geometric restrictions
Sylvain Ervedoza - CNRS, Institut de Mathématiques de Toulouse, UMR 5219, F-31062 Toulouse, France (email)
Abstract: The goal of this note is to explain how transmutation techniques (originally introduced in  in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in  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  on the frequency depending observability inequalities for waves without geometric restrictions, an iteration argument recently developed in  and the new representation formulas in  allowing to make a link between heat and wave trajectories.
Keywords: Heat equation, observability, transmutation.
Received: December 2010; Revised: March 2011; Available Online: June 2011.
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