Influence of the Domain Boundary on the Speeds of Traveling Waves

Lanxiang Ma, Jiale Tan

Department of Mathematics, Tongji University, Shanghai, China.
Ningbo Shentong Energy Co., Ltd., Ningbo, China.

DOI: 10.4236/am.2014.513203                

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 γ_t 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.

Keywords

Curvature Flow Equation, Traveling Wave, Average Speed, Spatial Heterogeneity

Conflicts of Interest

The authors declare no conflicts of interest.

References

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