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http://dx.doi.org/10.1016/j.jde.2008.01.014

has been cited by the following article:

• TITLE: Influence of the Domain Boundary on the Speeds of Traveling Waves

  AUTHORS: Lanxiang Ma, Jiale Tan

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

  JOURNAL NAME: Applied Mathematics, Vol.5 No.13, July 22, 2014

  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.