Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz–Minkowski plane R12

Abstract

In this paper, we investigate the evolution of spacelike curves in the Lorentz–Minkowski plane [Formula: see text] 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.