DG-MP-PDE Seminar: Juncheng Wei

Abstract:

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.)