Existence and Blowing-up of Solution of Wave Equation

The global existence of solution to the initial-boundary value problem of a nonlinear fourth-order wave equation with a damping term and a force source term was proved based on the standard semigroup theory and by introducing a modified energy function.The effects of nonlinear damping and force source term on blowing-up of the solution were analyzed with an energy-compensation method.The solution blows up in finite time under initial energy that is negative enough.The upper bound of life span for the solution was obtained.