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Stability results for the parameter identification inverse problem in cardiac electrophysiology

Abstract : In this paper we prove a stability estimate of the parameter identification problem in cardiac electrophysiology modeling. We use the monodomain model which is a reaction diffusion parabolic equation where the reaction term is obtained by solving an ordinary differential equation. We are interested in proving the stability of the identification of the parameter τ in which is the parameter that multiplies the cubic term in the reaction term. The proof of the result is based on a new Carleman-type estimate for both the PDE and ODE problems. As a consequence of the stability result we prove the uniqueness of the parameter τ in giving some observations of both state variables at a given time t 0 in the whole domain and the PDE variable in a non empty open subset w 0 of the domain.
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Submitted on : Friday, November 18, 2016 - 4:55:10 PM
Last modification on : Wednesday, June 2, 2021 - 9:48:21 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 8:33:29 AM

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Jamila Lassoued, Moncef Mahjoub, Nejib Zemzemi. Stability results for the parameter identification inverse problem in cardiac electrophysiology. Inverse Problems, IOP Publishing, 2016, 32 (11), pp.1-31. ⟨10.1088/0266-5611/32/11/115002⟩. ⟨hal-01399373⟩

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