带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度

本文提出并研究带有线性外力场的双曲平均曲率流，通过凸曲线的支撑函数，导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论，讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度（即局部解存在的最大时间区间）。

The lifespan of classical solution to the Cauchy problem for the hyperbolic mean curvature flow with a linear forcing term

We investigate the hyperbolic mean curvature flow with a linear forcing term. By means of support function, a hyperbolic Monge-Ampere equation is derived and this equation could be reduced to a system in Riemann invariants. Using the theory of the local solution to Cauchy problem for quasilinear hyperbolic system, we discuss the lifespan（the maximal existence time of unique local classical solutions） of classical solution to the Cauchy problem for the hyperbolic mean curvature flow with a linear forcing term.