生物介质中脉冲电场模型的适定性及其有限元逼近
Well-posedness of a Pulsed Electric Field Model in Biological Media and its Finite Element Approximation
摘要：
本文的工作旨在为分析脉冲电场对生物介质的影响提供一个数学和数值框架。生物组织和细胞悬浮液被描述为具有异质介电常数和异质电导率。建立了模型问题的适定性和解的正则性。本文提出了一种全离散有限元格式，用于对任意形状脉冲的电势分布同时作时间和空间函数的数值逼近，并证明了该格式在时间和空间上都具有最优收敛阶。所提出的数值方案在医学、食品科学和生物技术领域具有潜在的应用价值。
英文摘要：
This work aims at providing a mathematical and numerical framework for the analysis on the effects of pulsed electric fields on biological media. Biological tissues and cell suspensions are described as having a heteregeneous permittivity and a heteregeneous conductivity. Well-posedness of the model problem and the regularity of its solution are established. A fully discrete finite element scheme is proposed for the numerical approximation of the potential distribution as a function of time and space simultaneously for an arbitrary shaped pulse, and it is demonstrated to enjoy the optimal convergence order in both space and time. The proposed numerical scheme has potential applications in the fields of medicine, food sciences, and biotechnology.
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