Asymptotic behavior and blow-up of solutions to a nonlinear evolution equation of fourth order

In this paper, the asymptotic behavior of the solution to the initial–boundary value problem for a nonlinear evolution equation of fourth order equation(1)utt−a1uxx−a2uxxt−a3uxxtt=φ(ux)xutt−a1uxx−a2uxxt−a3uxxtt=φ(ux)x is studied. The sufficient conditions for blow-up of the solutions to the initial–boundary value problems for Eq. (1) are given.