DEGENERACY IN FINITE TIME OF 1D QUASILINEAR WAVE EQUATIONS II

We consider the large time behavior of solutions to the following nonlinear wave equation: partial derivative(2)(t)u=c(u)(2)partial derivative(2)(x)u+lambda c(u)c'(u)(partial derivative(x)u)(2) with the parameter lambda is an element of[0,2]. If c(u(0,x)) is bounded away from a positive constant, we can construct a local solution for smooth initial data. However, if c(.) has a zero point, then c(u(t,x)) can be going to zero in finite time. When c(u(t,x)) is going to 0, the equation degenerates. We give a sufficient condition that the equation with 0 <= lambda<2 degenerates in finite time.