一个模拟小动脉斑块的自由边界问题的分歧
Bifurcation for a free boundary problem modeling a small arterial plaque
摘要：
动脉粥样硬化，动脉硬化，起源于动脉中的小斑块;它是美国和世界范围内残疾和过早死亡的主要原因。本文研究了一个描述动脉粥样硬化早期斑块生长的高度非线性、高度耦合的偏微分方程模型的分支。该模型涉及LDL和HDL胆固醇、巨噬细胞以及泡沫细胞，其中分离斑块和血流区域的界面是自由边界。我们建立了从径向对称解分支出来的非对称破缺定态解的有限分支。由于斑块在现实中是不可能是严格的径向对称，我们的结果将是有用的，以解释斑块的不对称形状。
英文摘要：
Atherosclerosis, hardening of the arteries, originates from small plaque in the arteries; it is a major cause of disability and premature death in the United States and worldwide. In this paper, we study the bifurcation of a highly nonlinear and highly coupled PDE model describing the growth of arterial plaque 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 regions being a free boundary. We establish finite branches of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solution. Since plaque in reality is unlikely to be strictly radially symmetric, our result would be useful to explain the asymmetric shapes of plaque.
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