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题目：A Free Boundary Problem for Modeling Plaques in the Recent Progress

报告人：Prof. Bei Hu (University of Notre Dame)

时间：2023年10月26日 (星期四) 14：00—15：00

地点：致远楼101室

摘要：Atherosclerosis is a leading cause of death worldwide; it originates from a plaque which builds up in the artery. We considered a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. In an earlier work (with A. Friedman and W. Hao) of an extremely simplified model, we proved that there exist small radially symmetric stationary plaques and established a sharp condition that ensures their stability. In our work with Evelyn Zhao, we look for the existence of non-radially symmetric stationary solutions. The absent of an explicit radially symmetric stationary solution presents a big challenge to verify the Crandall-Rabinowitz theorem; through asymptotic expansion, we extend the analysis to establish a finite branch of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solutions. This work is further extended (with Xiaohong Zhang, Zhengce Zhang) to include to allow reverse cholesterol transport in the model. Extension in the longitude direction and combined logitude-latitude direction is recently carried out (with Yaodan Huang). A periodic small plaque solution was recently found (with Yaodan Huang). This solution is linearly stable under certain conditions (with Jingyi Liu).

报告人简介：Bei Hu, Professor in University of Notre Dame, Department of Applied and Computational Mathematics and Statistics. He is a famous PDE expert. His research interests include PDE elliptic and parabolic a priori estimates, variational inequalities, free boundary problems, reaction diffusion equations, singular perturbations, asymptotic analysis, homogenization approaches, optimal control in PDE problems, and their applications to industry, Biology and Mathematical finance. He wrote, translated and edited several books, published 120 academic papers, where many of them are in top journals.

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