Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology

Bedr'Eddine Ainseba; Mostafa Bendahmane; Yuan He; Bedr'Eddine Ainseba; Mostafa Bendahmane; Yuan He

doi:10.3934/nhm.2015.10.369

Networks and Heterogeneous Media

2015, Volume 10, Issue 2: 369-385. doi: 10.3934/nhm.2015.10.369

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Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology

1.
Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux, 3 ter Place de la Victoire, 33076 Bordeaux cedex
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received: 01 November 2013 Revised: 01 March 2015
Primary: 35K57, 35R30.

In this paper, we study the stability result for the conductivities diffusion coefficients to a strongly reaction-diffusion system modeling electrical activity in the heart. To study the problem, we establish a Carleman estimate for our system. The proof is based on the combination of a Carleman estimate and certain weight energy estimates for parabolic systems.
- Inverse problem,
- stability,
- reaction-diffusion system,
- cardiac electric field,
- Carleman estimates
Citation: Bedr'Eddine Ainseba, Mostafa Bendahmane, Yuan He. Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology[J]. Networks and Heterogeneous Media, 2015, 10(2): 369-385. doi: 10.3934/nhm.2015.10.369

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Abstract

In this paper, we study the stability result for the conductivities diffusion coefficients to a strongly reaction-diffusion system modeling electrical activity in the heart. To study the problem, we establish a Carleman estimate for our system. The proof is based on the combination of a Carleman estimate and certain weight energy estimates for parabolic systems.

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