Blow-up and decay for a class of pseudo-parabolic equation with p-Laplacian operator and nonlinearity source

We consider the following pseudo-parabolic equation ut−Δut−Δpu=|u|q−1u,x∈Ω,t>0 in a bounded domain with homogeneous Dirichlet boundary condition. We obtain result of global existence and establish the estimation of decay. We also provide sufficient conditions for the finite time blow-up of weak solutions by concavity methods, a upper bound estimation of the blow-up time is given. Moreover, by the means of a differential inequality technique, we obtain a lower bound for blow-up time.