Traveling waves of a curvature flow in almost periodic media. (English) Zbl 1182.35073

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.


35C07 Traveling wave solutions
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K93 Quasilinear parabolic equations with mean curvature operator
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