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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
