Blow-up of solutions of the nonlinear Sobolev equation

In this paper, we consider the nonlinear Sobolev equation u t − Δ u t − ( Δ q u ) t − Δ q u − Δ u − u p u x 1 = | u | 2 m u , with an initial condition and Dirichlet boundary condition. In different regions divided by p , q , and m , we obtain the sufficient conditions for finite-time blow-up of the solutions, and get the upper and lower bounds of the blow-up time.