Formation Of Singularities For Vibrating String Equation Of Mixed Initial-boundary Value Problems With Inhomogeneous Neumann Conditions

In this paper, we study the mixed initial-boundary value problems with inhomo-geneous Neumann boundary conditions for the nonlinear vibrating string equation on the strip:D={(t,x)|t≥0,0≤x≤l}. Under the assumptions that the bound-ary data are small and decaying and the initial data are small, we conclude that the classical solution must blow up in a finite time.