| Abstract: |
| We study the long-time behavior of driven curvature flow in a strip domain with periodic obstacles. In this setting, solutions exhibit two distinct behaviors: propagation and blocking. This talk characterizes how geometric features of the domain determine which behavior occurs.
In a strip domain with periodically undulating boundaries, Matano, Nakamura, and Lou (2006) characterized the long-time behavior of driven curvature flow in terms of the boundary geometry. They introduced the notion of a maximal opening angle to describe the conditions for propagation, blocking, and the propagation speed, under which global-in-time graph-like classical solutions exist. Later, Matano and Mori extended this analysis to more general settings where such classical solutions may fail to exist, and proposed the concept of an effective opening angle to characterize propagation and blocking phenomena.
In a strip domain with periodic obstacles, we introduce the notions of left and right opening angles, which are analogous to the effective opening angle. A key difference from previous studies lies in the propagation speed: while it is uniquely determined in earlier works, it is no longer unique in our setting. |
|