Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations
Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations
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DOI：
10.3934/dcds.2006.16.137
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发表时间：
2006-06
影响因子：
1.1
通讯作者：
Mitsunori Nara;M. Taniguchi
中科院分区：
文献类型：
--
作者：
Mitsunori Nara;M. Taniguchi
本文研究了二维空间中受恒动力曲率流控制的曲线的长时间演化行为。这个问题有两种类型的行波：行线和v形前，除了静止的圆。研究柯西问题，我们处理由x轴上的整个图表示的移动曲线。本文考虑曲线向v型锋面的均匀收敛。建立了一类空间非衰减初始扰动的收敛结果。我们的结果是正确的，没有假设给定扰动的小。
This paper is concerned with the long time behavior for evolution of a curve governed by a curvature flow with constant driving force in the two-dimensional space. This problem has two types of traveling waves: traveling lines and V-shaped fronts, except for stationary circles. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the $x$-axis. In this paper, we consider the uniform convergence of curves to the V-shaped fronts. Convergence results for a class of spatially non-decaying initial perturbations are established. Our results hold true with no assumptions on the smallness of given perturbations.