Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz-Minkowski plane ${\mathbb{R}}_1^2$

Abstract

In this paper, we investigate the evolution of spacelike curves in Lorentz-Minkowski plane ${\mathbb{R}}_1^2$ along prescribed geometric flows (including the classical curve shortening flow or mean curvature flow as a special case), which correspond to a class of quasilinear parabolic initial boundary value problems, and can prove that this flow exists for all time. Moreover, we can also show that the evolving spacelike curves converge to a spacelike straight line or a spacelike Grim Reaper curve as time tends to infinity.

11 pages. Comments are welcome

References in corpus (1)

• Self-similar solutions to the curve shortening flow