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Stability of Conductivities in an Inverse Problem in the Reaction-diffusion System in Electrocardiology

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAINSEBA, Bedr'Eddine
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierDepartment of Mathematics and Statistics [Lanzhou]
dc.contributor.authorYUAN, He
dc.date.issued2015-05-01
dc.identifier.issn1556-1801
dc.description.abstractEnIn 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. 1. Introduction. Let Ω ⊂ R N (N ≥ 1) be a bounded connected open set whose boundary ∂Ω is regular enough. Let T > 0 and ω be a small nonempty subset of Ω. We will denote (0, T) × Ω by Q T and (0, T) × ∂Ω by Σ T. To state the model of the cardiac electric activity in Ω (Ω ⊂ R 3 being the natural domain of the heart), we set u i = u i (t, x) and u e = u e (t, x) to represent the spacial cellular and location x ∈ Ω of the intracellular and extracellular electric potentials respectively. Their difference v = u i − u e is the transmembrane potential. The anisotropic properties of the two media are modeled by intracellular and extracellular conductivity tensors M i (x) and M e (x). The surface capacitance of the membrane is represented by the constant c m > 0. The transmembrane ionic current is represented by a nonlinear function h(v). The equations governing the cardiac electric activity are given by the coupled reaction-diffusion system: c m ∂ t v − div(M i (x)∇u i) + h(v) = f χ ω , in Q T , c m ∂ t v + div(M e (x)∇u e) + h(v) = gχ ω , in Q T , (1) where f and g are stimulation currents applied to Ω. We complete this model with Dirichlet boundary conditions for the intra-and extracellular electric potentials
dc.language.isoen
dc.publisherAmerican Institute of Mathematical Sciences
dc.title.enStability of Conductivities in an Inverse Problem in the Reaction-diffusion System in Electrocardiology
dc.typeArticle de revue
dc.identifier.doi10.3934/nhm.2015.10.xx
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.journalNetworks and Heterogeneous Media
bordeaux.peerReviewedoui
hal.identifierhal-01256802
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01256802v1
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