Periodic travelling wave solutions of a curvature flow equation in the plane

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概要

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• In the plane, we consider a curvature flow equation in heterogeneous media with periodic horizontal striations, the periodicity in space is expressed by periodic (in vertical direction) coefficients in the equation. We prove the existence and uniqueness of a curve which travels upward periodically with an average speed. At each time, the graph of the curve is a periodic undulating line at a finite distance from a straight line with a given inclination angle. We also show that the average speed depends on the inclination angle monotonously. Moreover, for homogenization problem as the spatial period tends to zero, we estimate the average speed by the inclination angle and some means of the periodic coefficients.

• 東北大学の論文

著者

• Lou Bendong

  Department Of Applied Mathematics Tongji University

関連論文

• Periodic travelling wave solutions of a curvature flow equation in the plane

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