Ill-posedness of nonlinear parabolic equation with critical initial condition

We study the initial boundary value problem of strongly nonlinear parabolic equation:∂u∂t=∑i=1N∂∂xi∂u∂xip−2∂u∂xi+u1+αwith critical initial data. By introducing a family of potential wells the global nonexistence of solution is proved, which solves the open problem existing in some classical literature.