关于剥脱现象的自由边值问题的研究

Study on a Free Boundary Value Problem Arising from Peeling Phenomenon

该文考虑一个产生于剥脱现象(Peeling Phenomenon)物理模型的自由边值问题其中弦振动的非线性效应已被考虑.这不同于K.Kikuchi,S.Omata等人曾研究的刻画Peeling Phenomenon的自由边值问题.作者在一些合理的假设下,证明了此问题局部经典解的存在唯一性.

In this paper the following free boundary problem {utt-x（ux/√1＋ux2）=0,{（t,x）｜t〉0,x〉-l0}∩{u〉0},1/2ut2＋1/√1＋ux2-1＋Q=0,{（t,x｜t〉0,x〉-l0}∩{u〉0}is considered. The problem describes the peeling phenomenon. Different from the problem studied by K. Kikuchi and S. Omata, the nonlinear effects in the vibrating string is also con- sidered. Under some reasonable assumptions, the local existence and uniqueness of classical solution for the free boundary problem is proved.