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<p>This paper presents a mathematical study of a nonlinear-coupled Thermistor–Navier–Stokes system modeling radiofrequency ablation in biological tissue considered as porous media. The model describes a three-phase flow system consisting of liquid, porous, and solid components. Using the Faedo-Galerkin method, we prove the existence and uniqueness of the weak solution. Furthermore, in establishing the a priori estimates, we show how the characteristics of the porous medium-namely, permeability and porosity affect the constants involved in the estimates. Finally, we provide numerical experiments that illustrate these dependencies and validate the theoretical results and motivations.</p>

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Well-posedness analysis and numerical simulation of a radiofrequency ablation model in a porous medium

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Y. Ouzrour,
  • M. Bendahmane,
  • Y. Ouakrim,
  • M. Zagour

摘要

This paper presents a mathematical study of a nonlinear-coupled Thermistor–Navier–Stokes system modeling radiofrequency ablation in biological tissue considered as porous media. The model describes a three-phase flow system consisting of liquid, porous, and solid components. Using the Faedo-Galerkin method, we prove the existence and uniqueness of the weak solution. Furthermore, in establishing the a priori estimates, we show how the characteristics of the porous medium-namely, permeability and porosity affect the constants involved in the estimates. Finally, we provide numerical experiments that illustrate these dependencies and validate the theoretical results and motivations.