Abstract:

The initial-boundary value problem of the four order nonlinear wave equation (known as beam equation) is considered in this paper. Under the condition that the initial energy E₀ is equal to the depth of potential well d, by constructing invariant sets, we obtain the sufficient conditions of the global existence and blow up of solutions for the nonlinear wave equation. Furthermore, the asymptotic properties of the global solutions have also been discussed.

Key words: Beam equation, Blow up, Global solutions, Asymptotic behavior