Global existence and blow-up of solutions for a higher-order Kirchhoff-type equation with nonlinear dissipation

This paper deals with the higher-order Kirchhoff-type equation with nonlinear dissipation u(tt) + (integral(Omega) \D(m)u\ dx)(q) (-Delta)(m)u + u(t)\u(t)\(r) = \u\(P)u, x is an element of Omega, t > 0, in a bounded domain, where m > 1 is a positive integer, q, p, r > 0 are positive constants. We obtain that the solution exists globally if p less than or equal to r, while if p > max{r, 2q}, then for any initial data with negative initial energy, the solution blows up at finite time in Lp+2 norm. (C) 2004 Elsevier Ltd. All rights reserved.