Study On A Free Boundary Value Problem Arising From Peeling Phenomenon

In this paper the following free boundary problem is considered. The problem describes the peeling phenomenon. It is different from the problem studied by K.Kikuchi and S.Omata, in which u satisfies the linear wave equation utt-uxx=0 in the domain{u>0}. They don't consider the nonlinear effects in the vibrating string. Our main results are:Starting from the physical model, we write the Lagrangian function when not making an approximation to the elastic potential, and derive its Euler-Lagrange equation. Denote the problem with the initial and boundary conditions by (P). Under some reasonable assumptions, we prove the local existence and uniqueness of classical solution for the problem (P).