Blow Up Of Solutions Of The Wave Equation With Mean Curvature Operator

In this paper,by using energy function,we consider the following initial-boundary value problem of the non-linear wave equation: where m≥1,b(t)=b0(t+1)-β,0≤β<1,b0>0.For linear damping case,based on two different methods,we study that the solution of the problem blows up in finite time when the initial energy E(0)≤0. In the nonlinear case,the solution of the problem blows up in finite time when the initial energy E(0)< 0 and E(0)< d (d is a positive value).At last,we prove the global existence when the initial value is under a certain condition.