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|
|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
|Date:||11 / 17 / 2008|
|Time:||03:35pm - 04:25pm|