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Matano, H., Nakamura, K.I. and Lou, B. (2006) Periodic Traveling Waves in a Two-Dimensional Cylinder with Saw-Toothed Boundary and Their Homogenization Limit. Networks & Heterogeneous Media, 1, 537-568.
https://doi.org/10.3934/nhm.2006.1.537

has been cited by the following article:

• TITLE: Periodic Travelling Waves of a Generalized Curvature Flow Arising from Crystal Growth Models

  AUTHORS: Haoran Li

  KEYWORDS: Periodic Traveling Wave, Generalized Curvature Flow, Average Speed

  JOURNAL NAME: Engineering, Vol.18 No.10, October 23, 2026

  ABSTRACT: In this paper, we consider a generalized curvature flow related to crystal growth in heterogeneous media with periodic oblique striations. The angle between the oblique striations and x -direction is α with 0<α<π/2 . We first prove the existence and uniqueness of periodic traveling waves that travel upward periodically with an average speed. Then, we derive the upper and lower bounds for the average speed of the periodic traveling wave.