Influence of the Domain Boundary on the Speeds of Traveling Waves

• 作者: Jiale Tan Lanxiang Ma
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: CURVATURE Flow Equation TRAVELING Wave AVERAGE SPEED Spatial HETEROGENEITY
• 年，卷（期）: 2014,（13）
• 页码范围: 2088-2097
• 页数: 10页
• 分类号: O1

摘要

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.