Math. Model. Nat. Phenom.
Volume 18, 2023
|Number of page(s)
|Mathematical physiology and medicine
|28 April 2023
On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bidomain model
Facultad de Ciencias en Física y Matemáticas-UNACH, Chiapas, Mexico
2 Facultad de Ciencias Físico Matemáticas-BUAP, Puebla, Mexico
* Corresponding author: firstname.lastname@example.org
Accepted: 3 March 2023
In this paper, we investigate the convergence of the Faedo-Galerkin approximations, in a strong sense, to a strong T-periodic solution of the torso-coupled bidomain model where T is the period of activation of the inner wall of the heart. First, we define the torso-coupled bidomain operator and prove some of its more important properties for our work. After, we define the abstract evolution system of the equations that are associated with torso-coupled bidomain model and give the definition of a strong solution. We prove that the Faedo-Galerkin’s approximations have the regularity of a strong solution, and we find that some restrictions can be imposed over the initial conditions, so that this sequence of Faedo-Galerkin fully converges to a strong solution of the Cauchy problem. Finally, these results are used for showing the existence a strong T-periodic solution.
Mathematics Subject Classification: 00-01 / 99-00
Key words: Bidomain model / Faedo-Galerkin scheme / variational formulation / weak and strong periodic solutions
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.