Blow-up of solution of Cauchy problem for three-dimensional damped nonlinear hyperbolic equation

The existence and uniqueness of the local generalized solution and the local classical solution to the Cauchy problem for three-dimensional damped nonlinear hyperbolic equation utt+k1∇4u+k2∇4ut+∇2g(∇2u)=0,u(x,0)=u0(x),ut(x,0)=u1(x) are proved. This paper arrives at some sufficient conditions for blow-up of the solution in finite time and an example.