Abstract
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.
Original language | English |
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Pages (from-to) | 137-156 |
Number of pages | 20 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 16 |
Issue number | 1 |
DOIs | |
Publication status | Published - Sep 2006 |
Externally published | Yes |
Keywords
- Convergence
- Curvature flow
- Traveling waves
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics