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

Abstract

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