Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary

Michel  Cristofol; Shumin  Li; Eric  Soccorsi

doi:10.3934/mcrf.2016009

Article Contents

2016, Volume 6, Issue 3: 407-427. Doi: 10.3934/mcrf.2016009

This issue Previous Article On the convergence of the Sakawa-Shindo algorithm in stochastic control Next Article Asymptotic stability of wave equations coupled by velocities

Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary

1.
Institut de Mathématiques de Marseille, CNRS, UMR 7373, École Centrale, Aix-Marseille Université, 13453 Marseille
2.
Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui Province, 230026
3.
Aix-Marseille Université de Toulon, CNRS, CPT, 13288 Marseille

Received: August 31, 2015

Revised: January 31, 2016

Published: August 2016

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Abstract

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Hölder stability with the aid of a Carleman estimate specifically designed for hyperbolic waveguides.

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Mathematics Subject Classification: Primary: 35R30, 35L30.

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