On the initial–boundary problem for fourth order wave equations with damping, strain and source terms

In this paper we study the global existence and blow-up of solutions to the fourth order equations utt+ut+Δ2u−αΔu−∑i=1n∂∂xi(θi(uxi))=f(u),x∈Ω,t>0, where α≥0α≥0.Under appropriate assumptions on the initial data and parameters in the above equation we establish two results on blow-up of solutions with arbitrary initial energy, −∞