论文标题
关于FAEDO-GALERKIN近似值与躯干耦合双域模型强的T型溶液的强烈收敛
On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bi-domain model
论文作者
论文摘要
在本文中，我们研究了Faedo-Galerkin近似值的收敛性，从很强的意义上讲，torso耦合的双域模型的强烈T型溶液，其中$ t $是心脏内壁激活的时期。首先，我们定义了躯干耦合的双域操作员，并证明了其工作中一些更重要的特性。之后，我们定义了与躯干耦合双域模型相关的方程式的抽象演化系统，并给出了强大解决方案的定义。我们证明Faedo-Galerkin的近似具有强大的解决方案的规律性，并且我们发现在初始条件下可以施加一些限制，因此Faedo-Galerkin的这种序列完全融合到Cauchy问题的全球强溶液中。最后，该结果用于显示存在强大的$ t $周期解决方案。
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.
