On the blow-up of a non-local parabolic problem

We investigate the conditions under which the solution of the initial-boundary value problem of the non-local equation ut=Δu+λf(u)/(∫Ωf(u)dx)p, where ΩΩ is a bounded domain of RNRN and f(u)f(u) is a positive, increasing, convex function, performs blow-up.