Mathematical Analysis of a Two-Dimensional Radiofrequency Ablation Model in Cardiac Tissue with $L^1$ Energy Dissipation

This paper deals with the existence and regularity of solutions for a nonlinear reaction-diffusion-fluid system that models radiofrequency ablation in cardiac tissue. The primary focus is on establishing the regularity of solutions in a two-dimensional setting, particularly in the presence of energy dissipation terms due to viscosity and electric fields, where these terms belong to the $L^1$ space. We rigorously establish the existence of global solutions for the system by employing the truncation approximation method, Schauder's fixed point theorem, and compactness arguments, under specific assumptions on the data. Finally, we present some numerical simulations to validate the theoretical findings.