Traveling curved fronts of a mean curvature flow with constant driving force.

*(English)*Zbl 0957.35124
Kenmochi, N. (ed.), Proceedings of the international conference on free boundary problems: theory and applications, Chiba, Japan, November 7-13, 1999. I. Tokyo: Gakkōtosho. GAKUTO Int. Ser., Math. Sci. Appl. 13, 206-221 (2000).

Summary: Traveling curved fronts by a mean curvature flow with constant driving force are studied. In the two-dimensional Euclidean space, the classification of all traveling fronts is completely carried out. It is proved that if the interface is a traveling front, then there are the following three possibilities: a line, a stationary circle, and a family of some traveling curved fronts. The explicit forms of all traveling curved fronts of this family are also obtained. It is proved that all traveling fronts can be represented by the graph except for stationary circles. Moreover we classify all traveling fronts in the half plane with a prescribed contact angle on the boundary. For higher dimensional Euclidean spaces, the existence of rotationally symmetric traveling curved fronts is obtained.

For the entire collection see [Zbl 0941.00020].

For the entire collection see [Zbl 0941.00020].

##### MSC:

35Q72 | Other PDE from mechanics (MSC2000) |

74N20 | Dynamics of phase boundaries in solids |

92E20 | Classical flows, reactions, etc. in chemistry |

82D55 | Statistical mechanics of superconductors |