小动脉斑块自由边界问题的第一歧点
On the first bifurcation point for a free boundary problem modeling small arterial plaque
摘要：
动脉粥样硬化发生在斑块阻塞动脉时。它是美国和世界范围内的主要死亡原因。本文研究了动脉粥样硬化早期斑块形成的高度非线性、高度耦合的偏微分方程模型的分支。该模型包括LDL和HDL胆固醇、巨噬细胞以及泡沫细胞，分离斑块和血流区域的界面是自由边界。建立了系统对应于$n=1$模式的第一个歧点。本文所研究的破环稳态解可能有助于理解为什么存在动脉斑块，该斑块通常在动脉的一侧比另一侧积累得更多。
英文摘要：
Atherosclerosis occurs when plaque clogs the arteries. It is a leading cause of death in the United States and worldwide. In this paper, we study the bifurcation for a highly nonlinear and highly coupled PDE model of plaque formation in the early stage of atherosclerosis. The model involves LDL and HDL cholesterols, macrophage cells as well as foam cells, with the interface separating the plaque and blood flow region being a free boundary. We establish the first bifurcation point for the system corresponding to $n=1$ mode. The symmetry-breaking stationary solution studied in this paper might be helpful in understanding why there exists arterial plaque that is often accumulated more on one side of the artery than the other.
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