Traveling waves of a curvature flow in almost periodic media (Q1032873)

The authors investigate travelling-wave solutions for a curvature-flow equation in a 2D media with almost periodic vertical striations (the heterogeneity). Two types of travelling waves are constructed: one having a straight line profile and the second having a V-shape profile. Interestingly, for the first type of travelling waves the profile is given by means of a function whose derivative is almost periodic (in the sense of H. Bohr), while the profile of the second type of travelling wave is quite similar to a pulsating cone, whose tails approach asymptotically profiles of first sort of travelling waves. Finally, an explicit expression for the averaged (homogenized) travelling wave speed is given.