In this paper, we consider the existence, both locally and globally in time, the decay and the blow-up of the solution for the higher-order Kirchhoff type equation:

At first, we prove the existence and uniqueness of the local solution based on the Banach contraction mapping principle. Then the decay estimates and global existence of the solution are proved by using Nakao’s inequality. At last, by ‘concavity’ method we establish three blow-up results for certain solutions in the case (i):  in the case (ii):  and in the case (iii):  At last, we consider that the estimation of the upper bounds of the blow-up time   for different initial energy.

higher-order nonlinear Kirchhoff equation, strong dissipation, local solutions, global solution, energy decay, degenerate case, non-degenerate case, blow-up.