PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng.

Title:Round droplet solutions and oval droplet solutions for the Ohta-Kawasaki theory and the Gierer-Meinhardt theory
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Xiaofeng Ren, The George Washington Univ
Abstract:
We consider a geometric problem that arises as a singular limit of the Ohta-Kawasaki theory of block copolymers and also of the Gierer-Meinhardt theory of morphogenesis. We first construct some solutions with a pattern of many round droplets. In the process a resonance condition, also known as the gap condition, appears and the main parameter of the problem must avoid these gaps for the round droplet solutions to exist. Further analysis near these resonance points reveals the existence of a second type of droplet solutions: Oval droplet solutions. On a generic domain these two types of droplet solutions explain a type of imperfect bifurcation and a saturation phenomenon.

Room Reservation Information

Room Number:MB216
Date:11 / 17 / 2008
Time:03:35pm - 04:25pm