On the initial–boundary problem for fourth order wave equations with damping, strain and source terms
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AbstractIn 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≥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, −∞<E(0)<+∞. Also, by using a potential well we show the global existence of solutions for the fourth order wave equation with some θi(s) and f(s). Especially, it is proved that the energy decays exponentially as t→∞.

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