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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    2,402 Downloads   2,872 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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