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.

翻译：本文提出一个模拟心脏组织内射频消融的非线性反应-扩散-流体系统。该模型描述了流体域和固体域内温度与电势的动态演化，以及固体域内速度的演化过程。通过构建涵盖固相与液相全域现象的方程组，我们针对包含广泛右端项的情形开展适定性分析。系统涉及热导率、运动黏度、电导率等参数，这些参数均表现出依赖于温度变量的非线性特性。数学分析延伸至三维空间全局解的存在性证明，采用Faedo-Galerkin方法。为增强理论结果的实践适用性，我们通过系列数值实验进行补充研究。采用有限元方法实现空间离散，时间离散采用欧拉格式。通过连续分析中引入的方程组解耦对非线性参数进行线性化处理。数值实验旨在验证并展示已建立的理论成果。