DG-MP-PDE Seminar: Juncheng Wei

  • Date: 03/01/2012
  • Time: 15:45
Juncheng Wei

University of British Columbia


Mathematical Analysis of Localized Patterns in Reaction-Diffusion Systems




I will describe some mathematical issues related to the
analysis of localized patterns (spikes and interfaces) in reaction
diffusion systems. For spikes, the analysis of the spectrum of various
classes of nonlocal eigenvalue problems (NLEP) is essential.  I will
discuss some new and interesting NLEPs arising in cross diffusion
systems and crime models. For interfaces, a nonlocal geometric problem
involving mean curvature and Newtonian potential is derived and
analyzed. Our goal is to give mathematically rigorous proofs of
existence and stability of various classes of patterns that have been
observed in experiments and simulations in the physics literature. Our
further goal is to predict the existence of some new patterns which have
not yet been found in experiments.  (Joint works with T. Kolokolnikov,
X. Ren, M. Ward, and M. Winter.)


Other Information: 

Note for Attendees: Refreshments will
be served in the PIMS Lounge from 3:30-3:45 p.m.


Location: WMAX 110