Tohoku Mathematical Journal

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

Bendong Lou

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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.

Article information

Tohoku Math. J. (2) Volume 59, Number 3 (2007), 365-377.

First available in Project Euclid: 11 October 2007

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Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 35B10: Periodic solutions

Periodic travelling wave solutions curvature flow equation homogenization problem


Lou, Bendong. Periodic travelling wave solutions of a curvature flow equation in the plane. Tohoku Math. J. (2) 59 (2007), no. 3, 365--377. doi:10.2748/tmj/1192117983.

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