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Influence of the Domain Boundary on the Speeds of Traveling Waves

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DOI: 10.4236/am.2014.513203    2,417 Downloads   2,893 Views  

ABSTRACT

Let H > 0 be a constant, g ≥ 0 be a periodic function and Ω ={(x, y) |x < H + g (y), y R}. We consider a curvature flow equation V = κ + A in Ω, where for a simple curve γt Ω, V denotes its normal velocity, κ denotes its curvature and A > 0 is a constant. [1] proved that this equation has a periodic traveling wave U, and that the average speed c of U is increasing in A and H, decreasing in max g' when the scale of g is sufficiently small. In this paper we study the dependence of c on A, H, max g' and on the period of g when the scale of g is large. We show that similar results as [1] hold in certain weak sense.

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Ma, L. and Tan, J. (2014) Influence of the Domain Boundary on the Speeds of Traveling Waves. Applied Mathematics, 5, 2088-2097. doi: 10.4236/am.2014.513203.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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