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Zbl 1182.35073
Lou, Bendong; Chen, Xinfu
Traveling waves of a curvature flow in almost periodic media. (English)
[J] J. Differ. Equations 247, No. 8, 2189-2208 (2009). ISSN 0022-0396

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.
[Adrian Muntean (Eindhoven)]

MSC 2000:: *35C07
35B27 Homogenization, etc.
35K93

Keywords: averaging; averaged wave speed

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