Videos

Logrithm Expansions and Refined Stability Thresholds for Multiple Spots in Reaction-diffusion Systems on a Two-dimensional Domain

Presenter
June 5, 2013
Keywords:
  • Reaction-Diffusion
MSC:
  • 35K57
Abstract
We consider the problem of refined stability thresholds for multiple spots in general reaction-diffusion systems (Gierer-Meinhardt, Schnakenberg, Gray-Scott,...). The stability thresholds given by Wei-Winter (2001, 2003) provide the leading logrithm order which doesnot depend on the location. Here we obtain the next O(1) term in terms of Green's function on the locations. We then combine with Floquet-Bloch theory to study which lattice of spots in the whole space is the most stable. (Joint work with D. Iron and M. Ward).