Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation

In this paper, we consider the nonlinear Kirchhoff-type equation $ u_{tt} + M(left| {D^m u(t)} right|_2^2 )( - Delta )^m u + left| {u_t } right|^{q - 2} u_t = left| {u_t } right|^{p - 2} u $ u_{tt} + M(left| {D^m u(t)} right|_2^2 )( - Delta )^m u + left| {u_t } right|^{q - 2} u_t = left| {u_t } right|^{p - 2} u with initial conditions and homogeneous boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time.