Carleman estimate for a linearized bidomain model in electrocardiology and its applications

Ionic parameters identification of an inverse problem of strongly coupled PDE’s system in cardiac electrophysiology using Carleman estimates

“…Our approach is based on a Carleman inequality for the bidomain reaction diffusion model coupled to a general form of ordinary differential equation system. This result is a step further in the parameters identification problem compared to the existing results [2,4,10,33,51]. There are two novelties in our result compared to the results in those paper.…”

“…The technics we shall discuss are similar to the framework using Carleman estimates for inverse problems but the obtained estimates differs from those of [17,44,53] because of the strongly coupled terms. We use the same strategy introduced by Wu and Yu in [51] to convert the strongly coupled terms to the gradient of the extra-cellular potential u e . Then, we consider the new version of the bidomain model as a whole to establish Carleman estimate under a weaker coupled equations.…”

Analysis of the heart-torso conductivity parameters recovery inverse problem in cardiac electrophysiology ECG modelling

“…In the computational electrophysiology community, the monodomain model is the most used in order that is computationally much cheaper than the bidomain model. In this context, there are some works focused to the study of the cardiac parameters identifiability problem by using Carleman estimates [1,2,29] and in the framework of the cardiac conductivities recovery problem by means of Carleman estimates, Aniseba, Bendahmane and Yuan in [3] obtains the stability results for the conductivities diffusion-coefficients and Wu, Yan, Gao and Chen in [41] proved a Holder stability result for the inverse conductivities problem.…”

Global uniqueness of an inverse problem for stochastic degenerate wave equation with three unknowns

“…The key tool to prove the inverse problem in this paper is Carleman estimate, which is a class of weighted energy estimates connected with deterministic/stochastic differential operators. Carleman estimate is applied to many aspects, such as the unique continuation property, 10,11 inverse problem, [12][13][14] and control theory. [15][16][17] There are numerous studies on inverse problems for deterministic hyperbolic equations by Carleman estimate, we refer to literature.…”