The Ohio State University Partial Differential Equations Seminar 

  Fall Semester 2022

Time/Location: Tuesdays 11:00-11:59 AM Virtual via Zoom or at MW154 (to be indicated below)

Schedule of talks:

Zoom Link for the Spring Semester 2022
Meeting ID: 948 6539 2210    Password: 314159
https://osu.zoom.us/j/94865392210?pwd=c2RpMGcwSWZtQXdxWHRXWFBKS3FYdz09


 
DATE  SPEAKER TITLE HOST(S)

Sep 6 

No seminar 
() 
   

Sep 13 

No seminar 
() 
   

Sep 20 

No seminar 
() 
   

Sep 27 

Bei Hu 
(Notre Dame) 
A Free Boundary Problem for modeling Plaques in the Artery – Recent progress  Friedman 

Oct 4 

No seminar 
() 
   

Oct 11 

Charis Tsikkou 
(West Virginia U.) 
  Keyfitz 

Oct 18 

No seminar 
() 
   

Oct 25 

Kazuo Yamazaki 
(Texas Tech) 
on ZOOM
  Fatheddin 

Nov 1 

Sze-bi Hsu 
(National Tsinghua Univ., Taiwan) 
  Lam 

Nov 8 

Robert De Jaco 
(NIST) 
  Keyfitz 

Nov 15 

Ivan Sudakow 
(Dayton) 
  Lam 

Nov 22 

No seminar 
() 
   

Nov 29 

No seminar 
() 
   

Dec 6 

No seminar 
() 
   

Dec 13 

No seminar 
() 
   

Abstracts

Bei Hu, Notre Dame (Sep 27, 2022)

Title: A Free Boundary Problem for modeling Plaques in the Artery – Recent progress

Abstract: 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.


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