On uniqueness theorems for the inverse problem of electrocardiography in the Sobolev spaces

DOI10.1002/zamm.202100217arXiv2111.03873OpenAlexW3213158242WikidataQ115240421 ScholiaQ115240421MaRDI QIDQ6202396

Unnamed Author, Konstantin S. Ushenin, Alexandre A. Shlapunov

Publication date: 26 March 2024

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.03873

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Inverse problems for PDEs (35R30)

Cites Work

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• Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology
• Optimal control of the bidomain system. II: Uniqueness and regularity theorems for weak solutions
• On 3D numerical inverse problems for the bidomain model in electrocardiology
• An iterative method for solving the Cauchy problem for elliptic equations
• Reaction-diffusion systems for the macroscopic bidomain model of the cardiac electric field
• Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
• On a mixed problem for the parabolic Lamé type operator
• Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology
• Deriving macroscopic myocardial conductivities by homogenization of microscopic models
• Carleman estimate for a linearized bidomain model in electrocardiology and its applications
• Thin sets in nonlinear potential theory
• Unfolding homogenization method applied to physiological and phenomenological bidomain models in electrocardiology
• Integrated heart -- coupling multiscale and multiphysics models for the simulation of the cardiac function
• The Cardiac bidomain model and homogenization
• The fast solution of boundary integral equations.
• On the possibility for computing the transmembrane potential in the heart with a one shot method: an inverse problem
• Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions
• Stability analysis of the inverse transmembrane potential problem in electrocardiography
• Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains
• Mixed elliptic boundary value problems
• Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model
• Bases With Double Orthogonality in the Cauchy Problem for Systems With Injective Symbols
• On the Cauchy problem for the elliptic complexes in spaces of distributions
• Multiscale Modeling for the Bioelectric Activity of the Heart
• Computing the Electrical Activity in the Heart
• An Infinite Dimensional Version of Sard's Theorem
• On Carleman-type Formulas for Solutions to the Heat Equation
• On a Transmission Problem Related to Models of Electrocardiology

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