Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 59, Number 3 (2007), 365-377.
Periodic travelling wave solutions of a curvature flow equation in the plane
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.
Tohoku Math. J. (2) Volume 59, Number 3 (2007), 365-377.
First available in Project Euclid: 11 October 2007
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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. https://projecteuclid.org/euclid.tmj/1192117983.