On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bi-domain model

TL;DR

This paper proves the strong convergence of Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bidomain model, establishing conditions for global convergence and existence of periodic solutions.

Contribution

It introduces a rigorous analysis of Faedo-Galerkin approximations for the bidomain model, demonstrating their strong convergence to periodic solutions under certain initial conditions.

Findings

Faedo-Galerkin approximations have the regularity of strong solutions.

Convergence of approximations to a global strong solution is established.

Existence of a strong T-periodic solution is proven.

Abstract

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 heart. First, we define the torso-coupled bi-domain operator and prove some of its more important properties for our work. After, we define the abstract evolution system of equations associated with torso-coupled bidomain model and give the definition of 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 converge to a global strong solution of the Cauchy problem. Finally, this results are used for showing the existence a strong $T$-periodic solution.