Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations

In this paper we investigate global existence, uniform decay and blow-up of solutions for the following Petrovsky equations: {utt+Δ2u+|ut|p−1ut=Fu(u,v),(x,t)∈Ω×[0,T),vtt+Δ2v+|vt|q−1vt=Fv(u,v),(x,t)∈Ω×[0,T), where ΩΩ is a bounded domain of Rn(n=1,2,3) having a smooth boundary and FF is a C1C1 function given by F(u,v)=α|u+v|r+1+2β|uv|r+12,r≥3,α>1,β>0. For the case of p=q=1p=q=1, we obtain the blow-up of solutions and the lifespan estimates for four different ranges of initial energy; for the case of 1