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Yasuhito Miyamoto

2008-01-16
14:10:00 - 15:00:00

On the shape of the stable patterns for activator-inhibitor systems

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

It is well-known that every inhomogeneous steady state of a scalar reaction-diffusion equation with the Neumann boundary condition is unstable provided that the domain is convex. It is also known that if an inhomogeneous steady state of a shadow reaction-diffusion system in a finite interval is stable, then it is monotone. In this talk, we consider the shape of the stable steady states to a shadow reaction-diffusion system of activator-inhibitor type in a disk. In particular, we give necessary conditions for a steady state to be stable, which can be determined by the shape.