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2007 Periodic travelling wave solutions of a curvature flow equation in the plane
Bendong Lou
Tohoku Math. J. (2) 59(3): 365-377 (2007). DOI: 10.2748/tmj/1192117983


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.


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Bendong Lou. "Periodic travelling wave solutions of a curvature flow equation in the plane." Tohoku Math. J. (2) 59 (3) 365 - 377, 2007.


Published: 2007
First available in Project Euclid: 11 October 2007

zbMATH: 1138.35035
MathSciNet: MR2365346
Digital Object Identifier: 10.2748/tmj/1192117983

Primary: 35K55
Secondary: 35B10, 35B27

Rights: Copyright © 2007 Tohoku University


Vol.59 • No. 3 • 2007
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