10:00 AM-10:50 AM
Kaoli (Salon 5)
Chair: Peter Bates, Brigham Young University, USA
A shadow system appears as a limit of a reaction-diffusion system in which some components have infinite diffusivity. It is known that unlike scalar reaction-diffusion equations, the shadow system exhibits various interesting phenomena such as spontaneous spatio-temporal pattern formation. On the other hand, it is also known that in autonomous shadow systems on a compact interval, any nonconstant non-monotone stationary solution is necessarily unstable. In this presentation, the speaker will discuss the dynamics of the shadow system in a general setting by applying the theory of Floquet bundles. The main conclusion is that any stable bounded (not necessarily stationary) solution is asymptotically homogeneous or eventually monotone in space.
Eiji Yanagida