Blow-up of solutions of the nonlinear Sobolev equation

In this paper, we consider the nonlinear Sobolev equation ut−Δut−(Δqu)t−Δqu−Δu−upux1=|u|2mu,ut−Δut−(Δqu)t−Δqu−Δu−upux1=|u|2mu, with an initial condition and Dirichlet boundary condition. In different regions divided by pp, qq, and mm, 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.