PDE seminar:Dynamics of Localized patterns for Reaction-Diffusion Systems on a Curved Surface

2014-4-7 16:30 - 2014-4-7 17:30
Faculty of Science Building #3, Room 309
Shin-Ichiro Ei (Hokkaido University)
The movement of a localized pattern appearing after Turing instability
is a much attractive topic. In this talk,
we consider reaction-diffusion systems which possess localized solutions
in two dimensional spaces and investigate the dynamics of the solutions
on a two dimensional curved surface. In order to analyze them, we
first assume the existence of a linearly stable localized solution in
the whole space and consider the movement of the solution when
the domain is deformed to a curved surface. By using the center
manifold reduction, we can reduce the dynamics to ODE systems expressed
by the gradient of Gaussian curvature.