Lorentz-Minkowski平面$\mathbb{R}^{2}_{1}$中一类拟线性抛物initial boundary value problems的平移解
Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$
摘要：
本文研究了Lorentz-Minkowski平面$\mathbb{R}^{2}_{1}$中类空曲线沿给定几何流（包括经典的曲线缩短流或中曲率流作为特例）的演化，这类曲线对应于一类拟线性抛物型初边值问题，并证明了这种流的存在性.此外，我们还可以证明，当时间趋于无穷大时，演化的类空曲线收敛于类空直线或类空死神曲线。
英文摘要：
In this paper, we investigate the evolution of spacelike curves in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
