We consider a mathematical model of the initiation and development of atherosclerosis in the early stage, defined in different domains. The existence of nonnegative weak solutions is proved via studying an auxiliary system with absolute value terms and applying a novel semi-discrete, operator splitting numerical scheme. Numerical simulations were performed in an idealized two-dimensional geometry in order to verify our assumptions in model building and theoretical analysis. The framework we developed can also be used for nonlinear reaction–diffusion systems defined in other different domains with more complex coupling conditions.

中文翻译：

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动脉粥样硬化早期数学模型的非负弱解

我们考虑在不同领域定义的早期动脉粥样硬化发生和发展的数学模型。通过研究具有绝对值项的辅助系统并应用一种新颖的半离散算子分裂数值格式，证明了非负弱解的存在。在理想化的二维几何中进行数值模拟，以验证我们在模型构建和理论分析中的假设。我们开发的框架还可用于具有更复杂耦合条件的其他不同领域中定义的非线性反应扩散系统。