### Sunday, August 13

## IP8

Dynamics of Shadow Systems

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**

*Graduate School of Mathematical Sciences*

*University of Tokyo, Japan*