This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.

中文翻译：

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新型心脏组织电热耦合射频模型的数学研究


本文提出了一种模拟心脏组织内射频消融的非线性反应扩散流体系统。该模型传达了流体和固体区域中温度和电势的动态演变，以及固体区域内速度的演变。通过制定描述整个领域（包括固相和液相）现象的系统，我们继续分析适定性，考虑广泛的右侧项。该系统涉及热导率、运动粘度和电导率等参数，所有这些参数都表现出取决于温度变量的非线性。数学分析扩展到在三维空间中采用 Faedo-Galerkin 方法来确定全局解的存在性。为了增强我们的理论结果的实际适用性，我们通过一系列数值实验来补充我们的研究。我们使用空间离散化的有限元方法和时间离散化的欧拉方案来实现离散系统。正如我们的连续分析中所介绍的，非线性参数通过解耦系统进行线性化。进行这些实验是为了证明和验证我们已经建立的理论结果。