| Abstract: |
| We consider blocking and propagation phenomena of mean curvature flow with a driving force in two-dimensional undulating cylinders with spatial periodicity. In this problem, Matano, Nakamura and Lou in 2006 prove the tmie global existence of the classical solutions under some boundary-slope condition that means the bumps of the boundary is not steep. Moreover they characterize the effect of the shape of the boundary to blocking and propagation by introducing a notion called maximal opening angle. However if we do not assume the boundary-slope condition, then the classical solutions do not always exist in time globally and their characterization by the maximal opening angle is not always applicable.
In this talk, we consider the effect of the shape of the boundary to blocking and propagation of this problem under more general situation that the solutions may develop singularities near the boundary. |
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