Global existence and blow-up of solutionsfor a higher-order kirchhoff-type equation with nonlinear dissipation Original Research Article

This paper deals with the higher-order Kirchhoff-type equation with nonlinear dissipation utt+q(∫Ω׀mDu׀2dx)m(−Δ)u+ut׀utr׀=׀up׀u,x∈Ω,t>0,utt+(∫Ω׀Dmu׀2dx)q(−Δ)mu+ut׀ut׀r=׀u׀pu,x∈Ω,t>0, Turn MathJax on in a bounded domain, where m < 1 is a positive integer, q, p, r < 0 arepositive constants. We obtain that the solution exists globally if p ≤ r, while ifp > max{r, 2q}, then for any initial data with negative initial energy, the solution blowsup at finite time in Lp+2 norm.