Observability of heat processes by transmutation without geometric restrictions

Ervedoza S, Zuazua E (2011)


Publication Type: Journal article

Publication year: 2011

Journal

Book Volume: 1

Pages Range: 177-187

Journal Issue: 2

DOI: 10.3934/mcrf.2011.1.177

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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APA:

Ervedoza, S., & Zuazua, E. (2011). Observability of heat processes by transmutation without geometric restrictions. Mathematical Control and Related Fields, 1(2), 177-187. https://dx.doi.org/10.3934/mcrf.2011.1.177

MLA:

Ervedoza, Sylvain, and Enrique Zuazua. "Observability of heat processes by transmutation without geometric restrictions." Mathematical Control and Related Fields 1.2 (2011): 177-187.

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