Blow Up And Existence To A Wave Equation With Source, Damping And Viscoelastic Terms

In this paper, By use of two different methods,we consider the cauchy problem of the non-linear wave equation with source, damping and viscoelastic terms inΩ(?)Rⁿwhere a, b > 0,p > 2, m≥1,Ωis a bounded domain of R^{n > l},with a smooth boundary (?)Ω.It is verified that,when the initial energy E(0)≤o,the solution of the problem is bound to blow up in finite time for linear damping equation. When the initial energy E(0) < d (d is a positive value), the solution of the problem is bound to blow up in finite time.We also discuss the global existence.