Tohoku Mathematical Journal

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

Bendong Lou

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Abstract

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

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

Dates
First available in Project Euclid: 11 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1192117983

Digital Object Identifier
doi:10.2748/tmj/1192117983

Mathematical Reviews number (MathSciNet)
MR2365346

Zentralblatt MATH identifier
1138.35035

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

Keywords
Periodic travelling wave solutions curvature flow equation homogenization problem

Citation

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.


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