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  

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

作　　者：王增桂[1] 

机构地区：[1]聊城大学数学科学学院,聊城252059

出　　处：《中国科学：数学》2013年第12期1193-1208,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11001115和11201473)资助项目

摘　　要：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-Amp`ere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).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.

关 键 词：线性外力场 双曲平均曲率流 双曲型 Monge-Ampère 方程 RIEMANN 不变量 生命跨度 

分 类 号：O186.11[理学—数学]