报告题目：A Free Boundary Problem for modeling Plaques in the Artery – Recent progress

报 告 人：胡钡， 美国圣母大学  教授

报告摘要：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 Avner Friedman and Wenrui 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 recent 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. Since plaque is unlikely to be strictly radially symmetric, our result would be useful to explain the asymmetric shapes of plaque. Our recent work (with Yaodan Huang, Xiaohong Zhang, Zhengce Zhang) extends to other possible shapes as well as more realistic modeling efforts.

报告人简介：胡钡教授现就职于美国University of Notre Dame，先后师从国内外偏微分方程领域的专家姜礼尚教授和Avner Friedman教授，多年来从事偏微分方程理论及其应用研究，尤其在抛物方程的爆破理论，生物医学中的自由边值问题的理论和数值以及具有金融背景的自由边界问题数值解的收敛性等研究领域中取得了丰富的研究成果，在Arch. Ration. Mech. Anal.、Comm. Partial Differential Equations、 Ann. Inst. H. Poincaré C Anal. Non Linéaire、SIAM J. Math. Anal.、SIAM J. Appl. Math. 、Math. Models Methods Appl. Sci.、Trans. Amer. Math. Soc.、J. Math. Biol.、J. Sci. Comput.、J. Differential Equations等国际著名期刊上发表高水平学术论文百余篇，被引用千余次。胡教授历任University of Notre Dame 数学系主任、理学院副院长等职，现任《Discrete Contin. Dyn. Syst. Ser. B》以及《Nonlinear Anal. Real World Appl.》编委，是国内外知名华人数学家。

报告时间：2022年10月15日（星期六）上午8:00-9:30（北京时间）

报告地点：Zoom Meeting ID：93004836589,密码：234042

主办单位：伟德国际1946源自英国