| Abstract: |
| Mean-curvature flow with a driving force appears in various mathematical problems such as motion of soap films, grain boundaries and singular limit problems of various reaction diffusion systems, e.g., Allen-Cahn-Nagumo equation. In this talk, we show the existence and uniqueness of traveling waves, composed of a Jordan curve (or closed surface), for an anisotropic curvature flow with a driving force. We call such a solution ``compact traveling wave in this talk. Our aim is to investigate the condition of external driving force when the curvature flow has traveling waves. This is a joint work with H. Ninomiya. |
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