Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
---|---|---|
Article Number | 14 | |
Number of page(s) | 25 | |
Section | Mathematical physiology and medicine | |
DOI | https://doi.org/10.1051/mmnp/2023012 | |
Published online | 28 April 2023 |
On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bidomain model
1
Facultad de Ciencias en Física y Matemáticas-UNACH, Chiapas, Mexico
2
Facultad de Ciencias Físico Matemáticas-BUAP, Puebla, Mexico
* Corresponding author: raul.felipe@unach.mx
Received:
14
March
2022
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
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